# (solved) Math 225N Week 8 FINAL EXAM

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## Math 225N Week 8 FINAL EXAM

**QUESTION 1**

A fitness center claims that the mean amount of time that a person spends at the gym per visit is 33 minutes. Identify the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the parameter μ.

Select the correct answer below:

H0: μ≠33; Ha: μ=33

H0: μ=33; Ha: μ≠33

H0: μ≥33; Ha: μ<33

H0: μ≤33; Ha: μ>33

**QUESTION 2**

The answer choices below represent different hypothesis tests. Which of the choices are **right-tailed** tests? Select all correct answers.

Select all that apply:

H0:X≥17.1, Ha:X<17.

H0:X=14.4, Ha:X≠14.4

H0:X≤3.8, Ha:X>3.8

H0:X≤7.4, Ha:X>7.4

H0:X=3.3, Ha:X≠3.3

**QUESTION 3**

Find the Type II error given that the null hypothesis, H0, is: a building inspector claims that no more than 15% of structures in the county were built without permits.

Select the correct answer below:

The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, no more than 15% of the structures really were built without permits.

The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures really were built without permits.

The building inspector thinks that more than 15% of the structures in the county were built without permits when, in fact, at most 15% of the structures were built without permits.

The building inspector thinks that no more than 15% of the structures in the county were built without permits when, in fact, more than 15% of the structures were built without permits.

**QUESTION 4**

Suppose a chef claims that her meatball weight is less than 4 ounces, on average. Several of her customers do not believe her, so the chef decides to do a hypothesis test, at a 10% significance level, to persuade them. She cooks 14 meatballs. The mean weight of the sample meatballs is 3.7 ounces. The chef knows from experience that the standard deviation for her meatball weight is 0.5 ounces.

- H0: μ≥4; Ha: μ<4
- α=0.1(significance level)

What is the test statistic (z-score) of this one-mean hypothesis test, rounded to two decimal places?

Provide your answer below:

$Test statistic =

**QUESTION 5**

What is the p-value of a **right-tailed** one-mean hypothesis test, with a test statistic of z0=1.74? (Do not round your answer; compute your answer using a value from the table below.)

Provide your answer below:

**QUESTION 6**

Kenneth, a competitor in cup stacking, claims that his average stacking time is 8.2 seconds. During a practice session, Kenneth has a sample stacking time mean of 7.8 seconds based on 11 trials. At the 4% significance level, does the data provide sufficient evidence to conclude that Kenneth’s mean stacking time is less than 8.2 seconds? Accept or reject the hypothesis given the sample data below.

- H0:μ=8.2 seconds; Ha:μ<8.2 seconds
- α=0.04(significance level)
- z0=−1.75
- p=0.0401

Select the correct answer below:

Do not reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04.

Reject the null hypothesis because the p-value 0.0401 is greater than the significance level α=0.04.

Reject the null hypothesis because the value of z is negative.

Reject the null hypothesis because |−1.75|>0.04.

Do not reject the null hypothesis because |−1.75|>0.04.

**QUESTION 7**

A recent study suggested that 81% of senior citizens take at least one prescription medication. Amelia is a nurse at a large hospital who would like to know whether the percentage is the same for senior citizen patients who go to her hospital. She randomly selects 59 senior citizens patients who were treated at the hospital and finds that 49 of them take at least one prescription medication. What are the null and alternative hypotheses for this hypothesis test?

Select the correct answer below:

{H0:p=0.81Ha:p>0.81

{H0:p≠0.81Ha:p=0.81

{H0:p=0.81Ha:p<0.81

{H0:p=0.81Ha:p≠0.81

**QUESTION 8**

A researcher claims that the proportion of cars with manual transmission is less than 10%. To test this claim, a survey checked 1000 randomly selected cars. Of those cars, 95 had a manual transmission.

The following is the setup for the hypothesis test:

{H0:p=0.10Ha:p<0.10

Find the test statistic for this hypothesis test for a proportion. Round your answer to 2 decimal places

Provide your answer below:

Test Statistic

**QUESTION 9**

A medical researcher claims that the proportion of people taking a certain medication that develop serious side effects is 12%. To test this claim, a random sample of 900 people taking the medication is taken and it is determined that 93 people have experienced serious side effects. .

The following is the setup for this hypothesis test:

*H*0:*p* = 0.12

*Ha*:*p* ≠ 0.12

Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.

The following table can be utilized which provides areas under the Standard Normal Curve:

z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |

-1.8 | 0.036 | 0.035 | 0.034 | 0.034 | 0.033 | 0.032 | 0.031 | 0.031 | 0.030 | 0.029 |

-1.7 | 0.045 | 0.044 | 0.043 | 0.042 | 0.041 | 0.040 | 0.039 | 0.038 | 0.038 | 0.037 |

-1.6 | 0.055 | 0.054 | 0.053 | 0.052 | 0.051 | 0.049 | 0.048 | 0.047 | 0.046 | 0.046 |

-1.5 | 0.067 | 0.066 | 0.064 | 0.063 | 0.062 | 0.061 | 0.059 | 0.058 | 0.057 | 0.056 |

-1.4 | 0.081 | 0.079 | 0.078 | 0.076 | 0.075 | 0.074 | 0.072 | 0.071 | 0.069 | 0.068 |

Provide your answer below:

P-value=

**QUESTION 10**

An economist claims that the proportion of people who plan to purchase a fully electric vehicle as their next car is greater than 65%.

To test this claim, a random sample of 750 people are asked if they plan to purchase a fully electric vehicle as their next car Of these 750 people, 513 indicate that they do plan to purchase an electric vehicle.

The following is the setup for this hypothesis test:

H0:p=0.65

Ha:p>0.65

In this example, the p-value was determined to be 0.026.

Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%.)

Select the correct answer below:

The decision is to reject the Null Hypothesis.

The conclusion is that there is enough evidence to support the claim.

The decision is to fail to reject the Null Hypothesis.

The conclusion is that there is not enough evidence to support the claim.

**QUESTION 11**

Becky’s statistics teacher was teaching the class how to perform the z-test for a proportion. Becky was bored because she had already mastered the test, so she decided to see if the coin she had in her pocket would come up heads or tails in a truly random fashion when flipped. She discretely flipped the coin 30 times and got heads 18 times.

Becky conducts a one-proportion hypothesis test at the 5% significance level, to test whether the true proportion of heads is different from 50%.

Which answer choice shows the correct null and alternative hypotheses for this test?

Select the correct answer below:

H0:p=0.6; Ha:p>0.6, which is a right-tailed test.

H0:p=0.5; Ha:p<0.5, which is a left-tailed test.

H0:p=0.6; Ha:p≠0.6, which is a two-tailed test.

H0:p=0.5; Ha:p≠0.5, which is a two-tailed test.

**QUESTION 12**

John owns a computer repair service. For each computer, he charges $50 plus $45 per hour of work. A linear equation that expresses the total amount of money John earns per computer is y=50+45x. What are the independent and dependent variables? What is the y-intercept and the slope?

Select the correct answer below:

The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.

John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45.

The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer.

John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50.

The independent variable (x) is the amount, in dollars, John earns for a computer. The dependent variable (y) is the amount of time John fixes a computer.

John charges a one-time fee of $50 (this is when x=0), so the y-intercept is 50. John earns $45 for each hour he works, so the slope is 45.

The independent variable (x) is the amount of time John fixes a computer. The dependent variable (y) is the amount, in dollars, John earns for a computer.

John charges a one-time fee of $45 (this is when x=0), so the y-intercept is 45. John earns $50 for each hour he works, so the slope is 50.

**QUESTION 13**

Ariana keeps track of the amount of time she studies and the score she gets on her quizzes. The data are shown in the table below. Which of the scatter plots below accurately records the data?

Hours studying | Quiz score |

1 | 5 |

2 | 5 |

3 | 7 |

4 | 9 |

5 | 9 |

Select the correct answer below:

**QUESTION 14**

Data is collected on the relationship between time spent playing video games and time spent with family. The data is shown in the table and the line of best fit for the data is y^=−0.27x+57.5. Assume the line of best fit is significant and there is a strong linear relationship between the variables.

According to the line of best fit, the predicted number of minutes spent with family for someone who spent 95 minutes playing video games is 31.85. Is it reasonable to use this line of best fit to make the above prediction?

Select the correct answer below:

The estimate, a predicted time of 31.85 minutes, is unreliable but reasonable.

The estimate, a predicted time of 31.85 minutes, is both unreliable and unreasonable.

The estimate, a predicted time of 31.85 minutes, is both reliable and reasonable.

The estimate, a predicted time of 31.85 minutes, is reliable but unreasonable.

**QUESTION 15**

Which of the following are feasible equations of a least squares regression line for the annual population change of a small country from the year 2000 to the year 2015? Select all that apply.

Select all that apply:

yˆ=38,000+2500x

yˆ=38,000−3500x

yˆ=−38,000+2500x

yˆ=38,000−1500x

**QUESTION 16**

True or false: The higher the average daily crops harvested, the closer to the peak of harvest it is.

Select the correct answer below:

True

False

**QUESTION 17**

An amateur astronomer is researching statistical properties of known stars using a variety of databases. They collect the color index, or B−V index, and distance (in light years) from Earth for 30 stars. The color index of a star is the difference in the light absorption measured from the star using two different light filters (a B and a V filter). This then allows the scientist to know the star’s temperature and a negative value means a hot blue star. A light year is the distance light can travel in 1 year, which is approximately 5.9 trillion miles. The data is provided below. Use Excel to calculate the correlation coefficient r between the two data sets, rounding to two decimal places.

Provide your answer below:

R= 0.18

**QUESTION 18**

The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars’ weights and mileage is collected. The table for the weight and mileage of the cars is given below. Use Excel to find the best fit linear regression equation, where weight is the explanatory variable. Round the slope and intercept to three decimal places.

Provide your answer below:

**QUESTION 19**

A farmer divided his piece of land into 4 equivalent groups. The quality of the soil is the same across the 4 groups of land. He planted the same crop in all 4 groups of land and recorded the yield of the crop in all 4 groups for a 4 week period. Is the study observational or experimental? If it is an experiment, what is the controlled factor?

Select the correct answer below:

The study is an observational study.

The study is an experiment. The controlled factor is the 4 week observation period.

The study is an experiment. The controlled factor is the land.

The study is an experiment. The controlled factor is the growth of the crops.

**QUESTION 20**

To test the effectiveness of a drug proposed to relieve symptoms of headache, physicians included participants for a study. They gave the drug to one group and a drug with no therapeutic effect to another group. Which group receives the placebo?

Select the correct answer below:

the physicians

the group that received the drug for headache

the group that received the drug with no therapeutic effect

all of the people in the study

**QUESTION 21**

A doctor notes her patient’s temperature in degrees Fahrenheit every hour to make sure the patient does not get a fever. What is the level of measurement of the data?

Select the correct answer below:

nominal

ordinal

interval

ratio

**QUESTION 22**

As a member of a marketing team, you have been tasked with determining the number of DVDs that people have rented over the past six months. You sample twenty adults and decide that the best display of data is a frequency table for grouped data. Construct this table using four classes.

15,31,28,19,14,18,28,19,10,19,10,24,14,18,24,27,10,18,16,23

Provide your answer below:

**QUESTION 23**

The histogram below displays the weights of rainbow trout (in pounds) caught by all visitors at a lake on a Saturday afternoon. According to this histogram, which range of weights (in pounds) contains the lowest frequency?

Provide your answer below:

greater than ……. but less than …..

**QUESTION 24**

Describe the shape of the given histogram.

Select the correct answer below:

uniform

unimodal and symmetric

unimodal and left-skewed

unimodal and right-skewed

bimodal

**QUESTION 25**

The bar graph below shows the number of boys and girls in different classes.

How many total students are in Ms. James’s class? Do not include the units in your answer.

Provide your answer below:

**QUESTION 26**

The line graph shown below represents the number of TVs in a house by square footage (in hundreds of feet). According to the information above, which of the following is an appropriate analysis of square footage and TVs?

Select the correct answer below:

From the data, the number of TVs doubled from a square footage of 8.5 and 10.

From the data, there is a steady decrease in the square footage and number of TVs.

From the data, there is a steady increase in the square footage and number of TVs.

From the data, when the square footage is between 8.5 and 10, the number of TVs remains the same.

**QUESTION 27**

Alice sells boxes of candy at the baseball game and wants to know the mean number of boxes she sells. The numbers for the games so far are listed below.

16,14,14,21,15

Find the mean boxes sold:

**QUESTION 28**

Given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median.

20,46,19,14,42,26,33

Provide your answer below:

Median:

**QUESTION 29**

Each person in a group shuffles a deck of cards and keeps selecting a card until a queen appears. Find the mode of the following number of cards drawn from a deck until a queen appears.

3,12,3,11,5,5,3,10,12

Provide your answer below:

Mode =

**QUESTION 30**

Given the following histogram, decide if the data is skewed or symmetrical.

Select the correct answer below:

The data are skewed to the left.

The data are skewed to the right.

The data are symmetric.

**QUESTION 31**

Which of the data sets represented by the following box and whisker plots has the smallest standard deviation?

Select the correct answer below:

A

B

C

D

**QUESTION 32**

The graph below shows the graphs of several normal distributions, labeled A, B, and C, on the same axis. Determine which normal distribution has the smallest standard deviation.

Select the correct answer below:

A

B

C

**QUESTION 33**

Brayden tosses a coin 500 times. Of those 500 times, he observes heads a total of 416 times. Calculations show that the probability of this occurring by chance is less than 0.01, assuming the coin is fair. Determine the meaning of the significance level.

Select the correct answer below:

We expect that 416 of every 500 coin tosses will result in heads.

At the 0.01 level of significance, the coin is likely not a fair coin.

There is certainty that the coin is not a fair coin.

The results are not statistically significant at the 0.05 level of significance.

**QUESTION 34**

Is the statement below true or false?

Independent is the property of two events in which the knowledge that one of the events occurred does not affect the chance the other occurs.

Select the correct answer below:

True

False

**QUESTION 35**

Of the following pairs of events, which pair has mutually exclusive events?

Select the correct answer below:

rolling a sum greater than 7 from two rolls of a standard die and rolling a 4 for the first throw

drawing a 2 and drawing a 4 with replacement from a standard deck of cards

rolling a sum of 9 from two rolls of a standard die and rolling a 2 for the first roll

drawing a red card and then drawing a black card with replacement from a standard deck of card

**QUESTION 36**

Fill in the following contingency table and find the number of students who both go to the beach AND go to the mountains.

Provide your answer below:

**QUESTION 37**

A statistics professor recently graded final exams for students in her introductory statistics course. In a review of her grading, she found the mean score out of 100 points was a x¯=77, with a margin of error of 10.

Construct a confidence interval for the mean score (out of 100 points) on the final exam.

Provide your answer below:

**QUESTION 38**

A random sample of adults were asked whether they prefer reading an e-book over a printed book. The survey resulted in a sample proportion of p′=0.14, with a sampling standard deviation of σp′=0.02, who preferred reading an e-book.

Use the empirical rule to construct a 95% confidence interval for the true proportion of adults who prefer e-books.

Provide your answer below:

**QUESTION 39**

The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?

z0.10 1.282 z0.05 1.645 z0.025 1.960 z0.01 2.326 z0.005 2.576

Use the table above for the z-score, and be sure to round up to the nearest integer.

Provide your answer below:

**QUESTION 40**

Which of the following frequency tables show a skewed data set? Select all answers that apply.

Select all that apply:

Value | Frequency |

5 | 1 |

6 | 2 |

7 | 10 |

8 | 11 |

9 | 17 |

10 | 17 |

11 | 15 |

12 | 12 |

13 | 7 |

14 | 7 |

15 | 0 |

16 | 1 |

Value | Frequency |

5 | 1 |

6 | 3 |

7 | 8 |

8 | 10 |

9 | 13 |

10 | 26 |

11 | 14 |

12 | 12 |

13 | 8 |

14 | 3 |

15 | 1 |

16 | 1 |

Value | Frequency |

12 | 1 |

13 | 1 |

14 | 3 |

15 | 6 |

16 | 23 |

17 | 29 |

18 | 19 |

19 | 15 |

20 | 3 |

Value | Frequency |

0 | 5 |

1 | 16 |

2 | 23 |

3 | 19 |

4 | 22 |

5 | 9 |

6 | 4 |

7 | 2 |

**QUESTION 41**

A poll was conducted during the final game of the basketball season to determine whether fans wanted to see the defending champions win the game or the challenging team win the game. From the poll, 216 of the 374 residents sampled from urban areas want the defending champions to win the game. In more rural areas, 304 of the 466 residents polled want the defending champions to win the game. Assuming location has nothing to do with team preference, the probability that the data gathered was the result of chance is calculated to be 0.03. What is the correct interpretation of this calculation?

Select the correct answer below:

More people from rural areas want the defending champions to win the game.

Exactly 216 out of every 374 urban residents want the defending champions to win the game.

The results are statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas.

The data is not statistically significant at the 0.05 level of significance in showing that the proportion of people in rural areas who want the defending champions to win the game is different than the proportion of people in urban areas.

**QUESTION 42**

In a psychological study aimed at testing a drug that reduces anxiety, the researcher grouped the participants into 2 groups and gave the anxiety-reduction pill to one group and an inert pill to another group. Which group receives the placebo?

Select the correct answer below:

the group that received the anxiety-reduction pill

the psychological study

all the people in the study

the group that received the inert pill

**QUESTION 43**

Which of the following results in the null hypothesis μ≥38 and alternative hypothesis μ<38?

Select the correct answer below:

A fitness center claims that the mean amount of time that a person spends at the gym per visit is at most 38 minutes.

A fitness center claims that the mean amount of time that a person spends at the gym per visit is fewer than 38 minutes.

A fitness center claims that the mean amount of time that a person spends at the gym per visit is 38 minutes.

A fitness center claims that the mean amount of time that a person spends at the gym per visit is more than 38 minutes.

**QUESTION 44**

True or False: The more shoes a manufacturer makes, the more shoes they sell.

Select the correct answer below:

True

False

**QUESTION 45**

Fill in the following contingency table and find the number of students who both do not play sports AND do not play an instrument.

Provide your answer below:

**QUESTION 46**

The answer choices below represent different hypothesis tests. Which of the choices are **left-tailed** tests? Select all correct answers.

Select all that apply:

H0:X=17.3, Ha:X≠17.3

H0:X≥19.7, Ha:X<19.7

H0:X≥11.2, Ha:X<11.2

H0:X=13.2, Ha:X≠13.2

H0:X=17.8, Ha:X≠17.8

**QUESTION 47**

Assume the null hypothesis, H0, is: Jacob earns enough money to afford a luxury apartment. Find the Type I error in this scenario

Select the correct answer below:

Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does.

Jacob thinks he does not earn enough money to afford the luxury apartment when, in fact, he does not.

Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does not.

Jacob thinks he earns enough money to afford the luxury apartment when, in fact, he does.

**QUESTION 48**

Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.

Select all that apply:

A has the larger mean.

B has the larger mean.

The means of A and B are equal.

A has the larger standard deviation.

B has the larger standard deviation.

The standard deviations of A and B are equal.

**QUESTION 49**

Hugo averages 74 words per minute on a typing test with a standard deviation of 11 words per minute. Suppose Hugo’s words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(74,11).

Suppose Hugo types 51 words per minute in a typing test on Wednesday. The z-score when x=51 is ________. This z-score tells you that x=51 is ________ standard deviations to the ________ (right/left) of the mean, ________.

Correctly fill in the blanks in the statement above.

Select the correct answer below:

Suppose Hugo types 51 words per minute in a typing test on Wednesday. The z-score when x=51 is 2.091. This z-score tells you that x=51 is 2.091 standard deviations to the **right **of the mean, 74.

Suppose Hugo types 51 words per minute in a typing test on Wednesday. The z-score when x=51 is 1.643. This z-score tells you that x=51 is 1.643 standard deviations to the **right **of the mean, 74.

Suppose Hugo types 51 words per minute in a typing test on Wednesday. The z-score when x=51 is −2.091. This z-score tells you that x=51 is 2.091 standard deviations to the left of the mean, 74.

Suppose Hugo types 51 words per minute in a typing test on Wednesday. The z-score when x=51 is −1.643. This z-score tells you that x=51 is 1.643 standard deviations to the **left **of the mean, 74.

**QUESTION 50**

The following frequency table summarizes a set of data. What is the five-number summary?

Value | Frequency |

2 | 4 |

5 | 2 |

9 | 1 |

10 | 1 |

12 | 1 |

13 | 4 |

18 | 3 |

19 | 1 |

22 | 1 |

23 | 1 |

Select the correct answer below:

Min | Q1 | Median | Q3 | Max |

2 | 10 | 11 | 20 | 23 |

Min | Q1 | Median | Q3 | Max |

2 | 5 | 9 | 18 | 23 |

Min | Q1 | Median | Q3 | Max |

2 | 6 | 17 | 20 | 23 |

Min | Q1 | Median | Q3 | Max |

2 | 5 | 6 | 13 | 23 |

Min | Q1 | Median | Q3 | Max |

2 | 5 | 13 | 18 | 23 |