1) The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24 ounces of cereal.At various times in the packaging process, we select a random sample of 100 boxes to see whether or not the machine is filling the boxes with an average of 24 ounces of cereal.

Which of the following is a statement of the alternative hypothesis?

Group of answer choices

a) The machine is not filling the boxes with the proper amount of cereal. The average is not 24 ounces.

b) The machine fills the boxes with the proper amount of cereal. The average is less than 24 ounces.

c) The machine fills the boxes with the proper amount of cereal. The average is 24 ounces.

Question 2

A sheet metal manufacturer is making 10-gauge sheet metal, which is supposed to be 3.416 mm thick. One of the pieces of manufacturing equipment was suspected of malfunctioning, so the manufacturer tested a random sample of 100 pieces of steel to make sure the average steel thickness is 3.416 mm.

Which of the following is a statement of the alternative hypothesis?

Group of answer choices

a) The equipment is not working properly. The average average steel thickness is not 3.416 mm.

b) The equipment is making the sheet metal too thick. The average average steel thickness is greater than 3.416 mm.

c)The equipment is working properly. The average average steel thickness is 3.416 mm.

Question 3

A government health official is interested in whether there has been a statistically significant decrease in teen smoking rates. In 2013, 8.4 percent of 12th graders had used tobacco in the past 30 days. With this data, we test the following hypotheses at the 5% significance level.

The health official surveys 200 randomly selected 12th graders and finds that 14 of them have used tobacco in the past 30 days.

H0: The percentage of 12th graders who have smoked in the past 30 days is equal to 8.4%.

Ha: The percentage of 12th graders who have smoked in the past 30 days is greater than 8.4%.

The p-value is 0.09. Which conclusion is correct?

Group of answer choices

a) Fail to reject H0.

b) Accept H0.

c) Reject H0.

Question 4

Does secondhand smoke increase the risk of a low birthweight? A baby is considered have low birthweight if he/she weighs less than 5.5 pounds at birth. According to the National Center of Health Statistics, about 7.8% of all babies born in the U.S. are categorized as low birthweight.

Suspecting that the national percentage is higher than 7.8%, researchers randomly select 1,200 babies whose mothers had extensive exposure to secondhand smoke during pregnancy and find that 10.4% of the sampled babies are categorized as low birth weight.

Let p be the proportion of all babies in the United States who are categorized as low birth weight. What are the appropriate null and alternative hypotheses for this research question?

Group of answer choices

a )H 0: p = 0.078

H a: p 0.078

b) H0: p = 0.078

Ha: p > 0.078

c) H0: p = 0.104

Ha: p 0.104

d) H0: = 0.078

Ha: > 0.078

Question 5

A quality control engineer at a potato chip company tests the bag-filling machine by weighing bags of potato chips. Not every bag contains exactly the same weight. But if more than 15% of bags are overfilled, then they stop production to fix the machine.

They define overfilled to be more than 1 ounce above the weight on the package. The engineer weighs 100 bags and finds that 21 of them are overfilled.

He plans to test the hypotheses: H0: p = 0.15 versus Ha: p > 0.15 (where p is the true proportion of overfilled bags). What is the test statistic?

Group of answer choices

a) Z = 1.68

b) Z = 4

c) Z = 1.68

d) Z = 1.47

Question 6 (SEE PHOTO ATTACHED)

A researcher wants to find out if U.S. adults still support the death penalty at a proportion of 0.64 (as it was in 2003). This graph indicates the sampling distribution for the proportion of supporters in random samples of 25 adults, as it would be if in fact p=0.64. The standard deviation of this sampling distribution is approximately 0.10.

What is the approximate test statistic for p = 0.84?

Group of answer choices

a) -2

b) -1

c) 0

d) 1

e) 2

Question 7

The proportion of college football players who have had at least one concussion is estimated to be 34% in the United States. We wanted to know if football players at our university were less likely to have suffered a concussion, so we surveyed a random sample of 100 past and present football players at our university. Is this survey valid or not valid for testing the hypothesis that the proportion of college football players at our university with at least one concussion is less than the national average?

Group of answer choices

a) Valid

b) Not Valid

Question 8

According to a U.S. news poll, 38% of students in the class of 2013 had done an internship during their time as an undergraduate student. Dana is interested in finding out whether students at her university had an internship rate that was higher than the national average. She obtained a list of 25 randomly selected students from the population of all students at her university by requesting this information from the university's institutional research office. She collected the responses and calculated that the proportion for her university was 43%.

Which one of the following statements about the z-test is correct?

Group of answer choices

a) It is safe to use the z-test for p.

b) It is not safe to use the z-test for p, since n * po is not large enough.

c) It is not safe to use the z-test for p, since the sample is not a random sample from the entire population (or cannot be considered as one).

d) It is not safe to use the z-test for p, since n * (1 po) is not large enough.

Question 9

Suppose that a major polling organization wanted to test the hypothesis that there was a change in the president's "approval rating" since last month. Last month, 35% of the representative sample of registered voters approved of the president. For this month, the null hypothesis was that the approval rating equals 35% and the alternative hypothesis is that the approval rating does not equal 35%. The significance level for this test was 0.05.

The results of the hypothesis test of the new survey showed a p-value of 0.008.

Which of the following statements is correct? Check all that apply.

Group of answer choices

a) The results were statistically significant.

b) The results were not statistically significant.

c) The null hypothesis should be rejected.

d) The null hypothesis should be accepted.

e) The null hypothesis cannot be rejected.

Question 10

According to Facebook's self-reported statistics, the average Facebook user has 130 Facebook friends. For a statistics project a student at Contra Costa College tests the hypothesis that CCC students will average more than 130 Facebook friends.

She randomly selects 3 classes from the schedule of classes and distributes a survey in these classes. Her sample contains 45 students.

Here are the null and alternative hypotheses for her study: H0: = 130, Ha: > 130.

What does represent in these hypotheses?

Group of answer choices

a) Mean number of Facebook friends for the average user.

b) Mean number of Facebook friends for CCC students

c) Mean number of Facebook friends for the CCC students in her sample

Question 11

In 2013, the average Girl Scout in New York City sold 96 boxes of cookies. The leader of Troop 5078 in New York City wants to know if the scouts in her troop sold more cookies than the average in New York City. She randomly samples 50 girls in Troop 5078 and records the number of boxes of cookies sold for each girl in the sample.

Here are the null and alternative hypotheses for her study: H0: = 96, Ha: > 96.

What does represent in these hypotheses?

Group of answer choices

a) Mean number of boxes of cookies sold for the Girl Scouts in Troop 5078

b) Mean number of boxes of cookies sold for the average Girl Scout in New York City

c) Mean number of boxes of cookies sold for the Girl Scouts in her sample from Troop 5078

Question 12

The Food and Drug Administration (FDA) is a U.S. government agency that regulates (you guessed it) food and drugs for consumer safety. One thing the FDA regulates is the allowable insect parts in various foods. You may be surprised to know that much of the processed food we eat contains insect parts. An example is flour.

When wheat is ground into flour, insects that were in the wheat are ground up as well. The mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. If the FDA finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption.

The FDA takes a random sample of 35 bags of flour for evaluation and finds that they contain an average of 80 insect parts per 100 grams, with a standard deviation of 6.3.

Which hypothesis test should be used to determine whether the sample contains more than the allowed 75 insect parts per 100 grams?

Group of answer choices

a) z-test for the population mean

b) t-test for the population mean

c) z-test for the population proportion

d) t-test for the population proportion

Question 13

The dean of the engineering school at a technical university wants to emphasize the importance of having students who are gifted at reading and writing as well as math. She wants to know if she can accurately claim that graduate students in engineering programs at her school have significantly higher scores on the verbal reasoning section of the GRE (a standardized test used in the admissions process for many graduate programs) than the national average for engineering students. The national average for the verbal reasoning GRE score for engineering students was 150 with a standard deviation of 9. A random sample of 49 engineering graduate students at her school were found to have an average verbal reasoning GRE score of 153.

What is the critical value of the test statistic used to determine whether the mean verbal reasoning GRE score of the engineering graduate students at the technical university is higher than the national average?

Group of answer choices

a) 136.33

b) 136.33

c) 2.33

d) 2.33

Question 14

A study was conducted to estimate , the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be = 3.6 hours.

A similar study conducted a year earlier estimated that , the mean number of weekly hours that U.S. adults use computers at home, was 8 hours. We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean has changed since the previous year.

Using a 95% confidence interval of (7.7, 9.3), which of the following is an appropriate conclusion?

Group of answer choices

a) The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.

b) The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls outside the confidence interval.

c) The current study does provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.

d) The current study does not provide significant evidence that the mean number of weekly hours has changed over the past year, since 8 falls inside the confidence interval.

d) You cannot draw a conclusion because the only way to reach a conclusion is to find the p-value of the test.

Question 15 (SEE PHOTO ATTACHED)

An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with the mean = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.

Below is the output:

Which of the following represents the correct conclusion we can make based on the output (and at the usual significance level of 0.05)?

Group of answer choices

a) The data provide enough evidence to reject 0

H

0

and to conclude that the mean volume per cup is lower than the target level of 10 oz.

b) The data provide enough evidence to accept 0

H

0

and to conclude that the mean volume per cup is at the target level of 10 oz.

c) The data do not provide enough evidence to reject 0

H

0

, so we accept it, and conclude that the mean volume per cup is at the target level of 10 oz.

d) The data do not provide enough evidence to reject 0

H

0

, nor to conclude that the mean volume per cup is lower than the target level of 10 oz.

Question 16 (SEE PHOTO ATTACHED)

In June 2005, a CBS News/NY Times poll asked a random sample of 1,111 U.S. adults the following question: "What do you think is the most important problem facing this country today?" Roughly 19% of those sampled answered "the war in Iraq" (while the rest answered economy/jobs, terrorism, healthcare, etc.). Exactly a year prior to this poll, in June of 2004, it was estimated that roughly 1 out of every 4 U.S. adults believed (at that time) that the war in Iraq was the most important problem facing the country.

We would like to test whether the 2005 poll provides significant evidence that the proportion of U.S. adults who believe that the war in Iraq is the most important problem facing the U.S. has decreased since the prior poll.

The following output is available for this test:

Group of answer choices

a) We have extremely strong evidence to reject 0

H

0

.

b) We have extremely strong evidence to reject

H

a

c) We have moderately strong evidence to reject 0

H

0

.

d) There is a probability of 0 that 0

H

0

is correct.

d) There is a probability of 0 that Ha is correct.

Question 17

Researchers at Gallup were interested in whether there was a decrease in the proportion of nonretirees (in other words, people who are not yet retired) who did not believe that the U.S. Social Security program will be able to pay them a retirement benefit when they retire. In the summer of 2010, the Gallup poll found that 60% of nonretirees thought that Social Security would not be able to pay a benefit. Five years later in the summer of 2015, Gallup asked the same question to 1,282 nonretirees and found that 51% of respondents did not think that Social Security would be able to pay a retirement benefit by the time that they retire.

We would like to test the hypothesis that in 2015 there is a lower proportion of nonretirees who do not think that Social Security will be able to pay them a benefit. A z-test for the population proportion showed that z = 4.29, p < 0.001.

Which of the following are the appropriate hypotheses in this case?

Group of answer choices

a) 0

H

0

: p = 0.51 vs.

H

a

: p < 0.51

b) 0

H

0

: p = 0.51 vs.

H

a

: p > 0.51

c) 0

H

0

: p < 0.60 vs.

H

a

: p = 0.60

d) 0

H

0

: p = 0.60 vs.

H

a

: p < 0.60

e) 0

H

0

: p = 0.60 vs.

H

a

: p 0.60

Question 18

An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally and should have the mean = 10 oz if it is working correctly. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.

In this problem, we have made slight changes to the "coffee machine" story above. In which of the options below is the change such that it would be inappropriate to conduct a hypothesis test for: H0: = 10 vs. Ha: < 10. Check all that apply.

Group of answer choices

a) An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean = 10 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.

b) An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean = 10 oz. A quality-control researcher randomly selects 40 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz. and the standard deviation is 0.23 oz.

c) An automatic coffee machine dispenses cups of coffee whose volume per cup varies normally with mean = 10 oz. and standard deviation = 0.23 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz.

d)An automatic coffee machine dispenses cups of coffee whose volume per cup varies according to a distribution with mean = 10 oz. and standard deviation = 0.23 oz. A quality-control researcher randomly selects 8 cups of coffee from the machine and finds that in this sample the mean volume is 9.92 oz.