# EBook Problems Hypothesis Basics

## EBook Problems Set - Fundamentals of Hypothesis Testing

### Problem 1

Suppose you were hired to conduct a study to find out which of two brands of soda college students think taste better. In your study, students are given a blind taste test. They rate one brand and then rated the other, in random order. The ratings are given on a scale of 1 (awful) to 5 (delicious). Which type of test would be the best to compare these ratings?

(a) One-Sample t
(b) Chi-Square
(c) Paired Difference t
(d) Two-Sample t

### Problem 2

USA Today's AD Track examined the effectiveness of the new ads involving the Pets.com Sock Puppet (which is now extinct). In particular, they conducted a nationwide poll of 428 adults who had seen the Pets.com ads and asked for their opinions. They found that 36% of the respondents said they liked the ads. Suppose you increased the sample size for this poll to 1000, but you had the same sample percentage who like the ads (36%). How would this change the p-value of the hypothesis test you want to conduct?

(a) No way to tell
(b) The new p-value would be the same as before
(c) The new p-value would be smaller than before
(d) The new p-value would be larger than before

### Problem 3

A marketing director for a radio station collects a random sample of three hundred 18 to 25 year-olds and two hundred and fifty 25 to 40 year-olds. She records the percent of each group that had purchased music online in the last 30 days. She performs a hypothesis test, and the p-value of her test turns out to be 0.15. From this she should conclude:

(a) that about 15% more people purchased on-line music in the younger group than in the older group.
(b) there is insufficient evidence to conclude that there is a difference in the proportion of on-line music purchases in the younger and older group.
(c) the proportion of on-line music purchasers is the same in the under-25 year-old group as in the older group.
(d) the probability of getting the same results again is 0.15.

### Problem 4

If we want to estimate the mean difference in scores on a pre-test and post-test for a sample of students, how should we proceed?

(a) We should construct a confidence interval or conduct a hypothesis test
(b) We should collect one sample, two samples, or conduct a paired data procedure
(c) We should calculate a z or a t statistic

### Problem 5

The paint used to make lines on roads must reflect enough light to be clearly visible at night. Let mu denote the true average reflectometer reading for a new type of paint under consideration. A test of the null hypothesis that mu = 20 versus the alternative hypothesis that mu > 20 will be based on a random sample of size n from a normal population distribution. In which of the following scenarios is there significant evidence that mu is larger than 20?

(i) n=15, t=3.2, alpha=0.05

(ii) n=9, t=1.8, alpha=0.01

(iii) n=24, t=-0.2, alpha=0.01

(a) (ii) and (iii)
(b) (i)
(c) (iii)
(d) (ii)

### Problem 6

The average length of time required to complete a certain aptitude test is claimed to be 80 minutes. A random sample of 25 students yielded an average of 86.5 minutes and a standard deviation of 15.4 minutes. If we assume normality of the population distribution, is there evidence to reject the claim? (Select all that applies).

• Choose at least one answer.
(a) No, because the probability that the null is true is > 0.05
(b) Yes, because the observed 86.5 did not happen by chance
(c) Yes, because the t-test statistic is 2.11
(d) Yes, because the observed 86.5 happened by chance

### Problem 7

We observe the math self-esteem scores from a random sample of 25 female students. How should we determine the probable values of the population mean score for this group?

(a) Test the difference in means between two paired or dependent samples.
(b) Test that a correlation coefficient is not equal to 0 (correlation analysis).
(c) Test the difference between two means (independent samples).
(d) Test for a difference in more than two means (one way ANOVA).
(e) Construct a confidence interval.
(f) Test one mean against a hypothesized constant.
(g) Use a chi-squared test of association.

### Problem 8

Food inspectors inspect samples of food products to see if they are safe. This can be thought of as a hypothesis test where H0: the food is safe, and H1: the food is not A. If you are a consumer, which type of error would be the worst one for the inspector to make, the type I or type II error?

(a) Type I
(b) Type II

### Problem 9

A college admissions officer is concerned that their admission criteria might not treat men and women with equal weight. To test this, the college took a random sample of male and female high school seniors from a very large local school district and determined the percent of males and females who would be eligible for admission at the college. Which of the following is a suitable null hypothesis for this test?

(a) p = 0.5
(b) The proportion of all eligible men in the district will not equal the proportion of all eligible women in the district.
(c) The proportion of all eligible men in the school district should be equal to the proportion of all eligible women in the school district.
(d) The proportion of eligible men sampled should equal the propotion of eligible women sampled.

### Problem 10

The average blood pressure for adults in the 30-40 year old age range is about 135. A researcher wonders whether the blood pressure of individuals with high stress positions differs from 135, keeping age range constant.

For a random sample of 120 people with high stress jobs, he found: X_bar = 137 p-value = 0.11 95% CI (139 to 141)

Based on these findings, he decided not to reject the null. Did he make the right decision?

(a) He did not make the right decision because his confidence interval does not include the hypothesized value under the null.
(b) The results reported by this researcher are inconsistent and contradictory.
(c) Yes, he made the right decision because the probability of rejecting the true null is 11%, and it is higher than the 5%.
(d) This researcher needs to report the standard deviation for his data.

### Problem 11

We want to determine if college GPAs differ for male athletes in major sports (e.g., football), minor sports (e.g., swimming), and intramural sports. What statistical method is most likely to be used to answer this question? Assume that all neccessary assumptions have been met for using this procedure.

(a) Test one mean against a hypothesized constant
(b) Test the difference in means between two paired or dependent samples
(c) test for a difference in more than two means (one way ANOVA)
(d) Test that a correlation coefficient is not equal to 0, correlation analysis
(e) Test the difference between two means(independent samples)

### Problem 12

In a one-way ANOVA with 3 groups, a rejection of the null hypothesis implies that:

(a) The 3 population means are equal to each other
(b) Each sample mean differs significantly from all other sample means
(c) Some subset of population means differs from some other subset of population means
(d) Each population mean differs significantly from all other population means
(e) The 3 sample means are equal to each other

### Problem 13

The journal Pediatrics compared the attempted suicide rates between youths who were adopted and those who were not. The null hypothesis is that the rates are the same, and the alternative is that those who were adopted have a higher suicide attempt rate. Which of the following is an example of a Type I error?

(a) The rates between adopted youth and non-adopted is the same, but the researchers reject the null hypothesis.
(b) The difference in rates between adopted youth and non-adopted youths is different in the sample than in the population.
(c) The rates between adopted youth and non-adopted are different, but researchers conclude they are the same.

### Problem 14

An after-school program in math is willing to renew its contract with a tutoring agency if the standardized math scores of the students increase by more than 10%. Over the last five years, 2000 students from the after-school program have attended this tutoring agency. In this context, what would happen if the after-school program makes a type II error?

(a) It makes a type II error if it continues working with the tutoring agency when the standardized math scores have not gone up at least 10%.
(b) It makes a type II error if it stops working with the tutoring agency when the standardized math scores have actually gone up at least 10%.
(c) It makes a type II error if it continues working with the tutoring agency when the standardized math scores have not gone up at most 10%.
(d) It makes a type II error if it stops working with the tutoring agency when the standardized math scores have actually gone up at most 10%.

### Problem 15

The standard medication for a certain disease is effective in 60% of all cases. A pharmaceutical company believes that its new drug is more effective than the standard treatment. Formulate the null and the alternative hypotheses to test whether there is statistical evidence to support the new drug.

(a) Ho: p=0.6; Ha: p>0.6
(b) Can't be determined without knowing the sample
(c) Ho: p<0.6; Ha: p=0.6
(d) Ho: p=0.6; Ha: p <0.6

### Problem 16

An experiment compares the taste of instant versus fresh-brewed coffee. Each subject tastes two unmarked cups of coffee in random order, one of each type, and states which he or she prefers. Of the 300 subjects who participate in the study, 114 prefer the instant coffee. Is there statistically significant evidence in the sample to support the suspicion that a majority of people prefer the taste of fresh-brewed coffee? Write the null and the alternative hypotheses for this test.

(a) Ho: p=0.5; Ha: p < 0.5
(b) Ho: p=0.5; Ha: p>0.5
(c) Ho: p =0.6; Ha: p <0.6
(d) Ho: p=0.38; Ha: p < 0.38

### Problem 17

A team of sociologists is investigating attitudes towards religion. In particular, they wish to examine differences in attitudes between the genders. They take a random sample of 400 married couples, and ask both people in the couple: "Do you believe in a literal heaven and hell?". About 55% of the women and 54% of the men said that they did believe. The sociologists wish to perform a hypothesis test to test whether the percent of men who believe in a literal heaven and hell in the population is the same as the percent of women. Which of the following statements is true?

(a) You should not perform a two-sample proportion test because the sample size is not sufficient.
(b) You should not perform a two-sample proportion test because the samples are not independent.
(c) A two-sample proportion test is appropriate because the sample size is less than 10% the population size.

### Problem 18

A company is sued for job discrimination because only 19% of the newly hired candidates were minorites when 27% of all applicants were minorities. The lawyers will perform a hypothesis test to test whether the company's hiring practices are discriminatory. How will the power of the test compare if the test is done at the 5% level of significance as opposed to the 1% level of significance?

(a) The power depends on the sample size and will therefore be the same at either level
(b) the power will be less at the 5% level than at the 1% level
(c) The power will be greater at the 5% level than at the 1% level
(d) The power depends on the difference between the true percentage of minority applicants and will therefore be the same at both significance levels

### Problem 19

A manufacturer of automobiles purchases machine bolts from a supplier who claims that no more than 5% of his bolts are defective. The manufacturer suspects that this claim is false. From a random sample of 400 bolts, the manufacturer found that 28 are defective. Is there suficient evidence to reject the supplier's claim?

(a) No, because the z is 0.07
(b) No, because the z is 1.851
(c) Yes, because the z is 1.851
(d) Yes, because the z is 0.07

### Problem 20

When a roulette wheel is perfectly balanced, in the long run red numbers should turn up 18 times in 38 spins. To test its wheel, one casino records the results of 3,800 plays, finding 1,000 red numbers. Based on how a roulette wheel is supposed to work, is that too few reds? Test at the 0.05 level.

(a) No, because the p-value is less than 0.05
(b) No, because the p-value is bigger than 0.05
(c) Yes, the p-value is more than 0.05
(d) Yes, the p-value is less than 0.05

### Problem 21

When you set the significance level for a hypothesis test, what are you controlling for?

(a) Type II error
(b) Type I error
(c) The critical value
(d) The t-value

### Problem 22

When conducting a formal hypothesis test, there are different errors that may be made, depending on your decision. One decision is to reject the null hypothesis. If you falsely reject the null hypothesis, what type of error has been made?