Hypothesis Testing for Proportions: Interactive Learning Quizzes

Question 1

A confidence interval for a population proportion is calculated to be (0.45, 0.55). What is the margin of error for this confidence interval?

Accepted Answer

0.05

Answer

0.1

Question 2

A company believes that the proportion of their customers who are repeat customers is higher than 40%. What type of alternative hypothesis should they use in a hypothesis test?

Accepted Answer

H1: p > 0.4

Question 3

Which of the following is a correct interpretation of a p-value of 0.05 in a hypothesis test about a population proportion?

Accepted Answer

There is a 5% chance that the null hypothesis is true.

Answer

There is a 95% chance that the null hypothesis is true.

Question 4

In hypothesis testing for proportions, what is the purpose of calculating the z-score?

Accepted Answer

To standardize the sample proportion and make it comparable to the hypothesized proportion.

Answer

To calculate the margin of error for the confidence interval.

Question 5

A study determines that the proportion of female students in a university is 0.6. A 95% confidence interval for this proportion is computed to be (0.56, 0.64). What does this interval represent?

Accepted Answer

The probability that the true population proportion lies between 0.56 and 0.64

Answer

The probability that the sample proportion will fall between 0.56 and 0.64 in the long run

Answer

The range within which the true population proportion is guaranteed to fall

Answer

The proportion of female students in the sample

Question 6

Which of the following is NOT an assumption for conducting a z-test for proportions?

Accepted Answer

The population is normally distributed

Answer

The sample size is sufficiently large

Answer

The sample is randomly selected

Answer

The expected number of both successes and failures is at least 10

Question 7

A survey finds that 25% of college students have a part-time job. A researcher wants to test if this proportion differs from 30%. Which hypothesis test is appropriate?

Accepted Answer

One-sample z-test

Answer

Two-sample z-test

Answer

Chi-square test

Answer

t-test

Question 8

Which formula represents the standard error of a sample proportion?

Accepted Answer

√(p * q / n)

Answer

p * q / n

Answer

√(n * p * q)

Answer

(p + q) / n

Question 9

What is the formula to calculate the sample proportion?

Accepted Answer

p = X / n

Answer

p = n / X

Answer

p = X / X

Answer

p = n / n

Question 10

What is the confidence level represented by a 95% confidence interval?

Accepted Answer

0.95

Answer

0.90

Answer

0.98

Answer

0.99

Question 11

Which of the following is the formula to calculate the standard error for a proportion?

Accepted Answer

√(p * (1-p) / n)

Answer

√(p * (1-p))

Answer

p * (1-p) / n

Answer

p / √(n)

Question 12

Which of the following is a correct interpretation of the following confidence interval: (0.58, 0.72)?

Accepted Answer

With 90% confidence, we can say that the true population proportion is between 0.58 and 0.72.

Answer

With 90% confidence, we can say that the sample proportion is between 0.58 and 0.72.

Answer

The probability of the true population proportion being between 0.58 and 0.72 is 90%.

Answer

We can be 90% certain that the sample is representative of the population.

Question 13

A survey claims that 38% of adults in the US own a pet. A random sample of 450 adults is taken, and 195 of them own pets. Calculate the margin of error for a 95% confidence interval.

Accepted Answer

0.058

Answer

0.048

Answer

0.068

Answer

0.078

Question 14

Which of the following is NOT an assumption of hypothesis testing for proportions?

Accepted Answer

Sample size must be less than 5% of the population size

Answer

Random sample

Answer

Independence of observations

Answer

Normally distributed population

Question 15

What is the distinction between a one-tailed and two-tailed hypothesis test?

Accepted Answer

In a one-tailed test, the alternative hypothesis specifies a directional prediction, while in a two-tailed test, it does not.

Answer

A one-tailed test has a smaller critical value than a two-tailed test.

Answer

The null hypothesis is not specified in a one-tailed test.

Answer

There is no difference in the interpretation of results between one-tailed and two-tailed tests.

Question 16

Which formula represents the confidence interval for a population proportion?

Accepted Answer

p +/- z * √(p(1-p)/n)

Answer

p +/- t * √(p(1-p)/n)

Answer

p +/- z * √(p/n)

Answer

p +/- t * √(p/n)

Question 17

Which advantage does a confidence interval offer over a hypothesis test?

Accepted Answer

Confidence intervals provide a range of plausible values for the population parameter.

Answer

Confidence intervals require a smaller sample size than hypothesis tests.

Answer

Confidence intervals are always more precise than hypothesis tests.

Answer

There are no advantages of using a confidence interval over a hypothesis test.

Question 18

How does the sample size affect the width of a confidence interval?

Accepted Answer

As the sample size increases, the width of the confidence interval decreases.

Answer

As the sample size decreases, the width of the confidence interval increases.

Answer

The sample size does not influence the width of the confidence interval.

Answer

The relationship between sample size and confidence interval width depends on the population standard deviation.

Question 19

What is the role of a confidence level in hypothesis testing?

Accepted Answer

To control the probability of making a Type I error.

Answer

To control the probability of making a Type II error.

Answer

To estimate the population standard deviation.

Answer

To determine the p-value.

Question 20

Which of the following formulas represents the z-test for a proportion?

Accepted Answer

z = (p̂ - p₀) / √((p̂ * (1 - p̂)) / n)

Answer

z = (p̂ - p₀) / √((p₀ * (1 - p₀)) / n)

Answer

z = (p̂ * (1 - p̂)) / √((p₀ * (1 - p₀)) / n)

Answer

z = (p₀ * (1 - p₀)) / √((p̂ * (1 - p̂)) / n)

Question 21

A survey finds that 45% of customers are satisfied with a new product. If the population proportion is 0.4, is this a statistically significant difference at a significance level of 0.05?

Accepted Answer

Yes

Answer

No

Answer

Cannot be determined

Question 22

What is the confidence level associated with a 95% confidence interval?

Accepted Answer

95%

Answer

90%

Answer

99%

Answer

100%

Question 23

Which of the following factors does NOT affect the width of a confidence interval for a proportion?

Accepted Answer

Significance level

Answer

Sample size

Answer

Confidence level

Answer

Population proportion

Question 24

What is the sample size required for a z-test for a proportion to have a margin of error of 0.05 and a confidence level of 95%?

Accepted Answer

384

Answer

768

Answer

1536

Answer

3072

Question 25

What is the p-value of a z-test for a proportion?

Accepted Answer

The probability of obtaining the observed sample proportion, assuming the null hypothesis is true

Answer

The probability of rejecting the null hypothesis, assuming the null hypothesis is true

Answer

The probability of making a Type I error

Answer

The probability of making a Type II error

Question 26

Which of the following is the correct null and alternative hypotheses for testing if the proportion of defective products is less than 5%? (p < 0.05)

Accepted Answer

H0: p ≥ 0.05, Ha: p < 0.05

Answer

H0: p < 0.05, Ha: p = 0.05

Answer

H0: p = 0.05, Ha: p > 0.05

Answer

H0: p > 0.05, Ha: p < 0.05

Question 27

A survey finds that 45% of consumers prefer product A. If the confidence level is 95% and the margin of error is 5%, what is the required sample size?

Accepted Answer

385

Answer

770

Answer

1540

Answer

193

Question 28

What is the correct interpretation of a confidence interval for a population proportion?

Accepted Answer

The interval contains all possible values of the population proportion with a specified level of confidence.

Answer

The population proportion will always fall within the confidence interval.

Question 29

A company survey finds that 75% of customers are satisfied with its customer service. After implementing a new customer service training program, a follow-up survey is conducted. Which scenario suggests a significant improvement?

Accepted Answer

A 95% confidence interval for the proportion of satisfied customers after the training is (0.8, 0.9).

Answer

The sample proportion of satisfied customers after the training is 0.85.

Question 30

A restaurant manager wants to test if the proportion of customers who order desserts is more than 0.4. A sample of 250 customers is surveyed, and 125 of them order desserts. Calculate the p-value for this test.

Accepted Answer

0.002

Answer

0.02

Answer

0.05

Answer

0.1

Question 31

What is the most appropriate guideline for writing the conclusion of a hypothesis test on a population proportion?

Accepted Answer

Clearly state whether the null hypothesis is rejected or not rejected, then interpret the results in the context of the research question.

Answer

Provide a detailed explanation of the statistical calculations.

Question 32

A company claims that the proportion of its customers who are satisfied with its customer service is 0.9. A consumer protection agency wants to investigate this claim. A random sample of 300 customers is taken, and 240 of them express satisfaction. Calculate the p-value for the hypothesis test.

Accepted Answer

0.0004

Answer

0.04

Answer

0.004

Answer

0.4

Question 33

A company claims that at least 80% of its customers are satisfied with its products. A random sample of 100 customers revealed that 72 were satisfied. At a 5% significance level, what is the conclusion of the hypothesis test?

Accepted Answer

Reject the null hypothesis. There is sufficient evidence to conclude that less than 80% of customers are satisfied.

Answer

Fail to reject the null hypothesis. There is not enough evidence to conclude that less than 80% of customers are satisfied.

Question 34

A political party wants to estimate the proportion of voters who support their candidate. They conduct a survey of 400 randomly selected voters and find that 220 support their candidate. Calculate the 95% confidence interval for the population proportion.

Accepted Answer

(0.495, 0.585)

Answer

(0.505, 0.575)

Answer

(0.485, 0.595)

Answer

(0.515, 0.565)

Question 35

A marketing firm claims that their new advertising campaign will increase website traffic by at least 15%. To test this claim, they track website visits before and after the campaign.  What type of hypothesis test should be used?

Accepted Answer

Paired t-test for proportions

Answer

Chi-square test for independence

Answer

Two-sample z-test for proportions

Answer

One-sample z-test for proportions

Question 36

A researcher wants to determine if there is a significant difference in the proportion of men and women who prefer a particular brand of coffee.  What is the null hypothesis for this test?

Accepted Answer

The proportion of men who prefer the brand is equal to the proportion of women who prefer the brand.

Answer

The proportion of men who prefer the brand is less than the proportion of women who prefer the brand.

Answer

The proportion of men who prefer the brand is greater than the proportion of women who prefer the brand.

Question 37

A company is conducting a survey to determine the proportion of customers who are satisfied with their customer service.  They want to be 99% confident that the sample proportion is within 3% of the true population proportion.  What is the minimum sample size needed?

Accepted Answer

1068

Answer

159

Answer

534

Answer

253

Question 38

A p-value of 0.02 in a hypothesis test for proportions indicates:

Accepted Answer

There is a 2% chance of observing the sample results if the null hypothesis is true.

Answer

There is a 2% chance that the null hypothesis is true.

Answer

There is a 98% chance of observing the sample results if the null hypothesis is true.

Question 39

A company is testing a new marketing campaign to increase online sales. They randomly assign customers to either the control group (no campaign) or the treatment group (new campaign).  The results show that 10% of the control group made a purchase, while 15% of the treatment group made a purchase. What is the appropriate hypothesis test to determine if the new campaign is effective?

Accepted Answer

Two-sample z-test for proportions

Answer

Chi-square test for goodness of fit

Answer

One-sample z-test for proportions

Answer

Paired t-test for proportions

Question 40

A researcher is interested in determining if the proportion of students who use social media to study has increased from 60% in the past year.  What is the alternative hypothesis for this test?

Accepted Answer

The proportion of students who use social media to study is greater than 60%.

Answer

The proportion of students who use social media to study is different from 60%.

Answer

The proportion of students who use social media to study is less than 60%.

Question 41

A company claims that 90% of its customers are satisfied with their products. A consumer advocacy group wants to test this claim and collects data from a random sample of 200 customers. They find that 170 customers are satisfied.  What is the test statistic for this hypothesis test?

Accepted Answer

-2.53

Answer

2.53

Answer

-1.96

Answer

1.96

Question 42

A company is conducting a market research study to determine the proportion of consumers who prefer a new product design. They want to ensure that the margin of error is no more than 2% with a 95% confidence level.  What is the minimum sample size needed?

Accepted Answer

2401

Answer

1201

Answer

601

Answer

301

Question 43

A market research firm wants to know if the proportion of adults who prefer brand A over brand B is greater than 0.5. They conduct a survey and observe that 65% of the respondents prefer brand A. Assuming a sample size of 200, what is the null hypothesis?

Accepted Answer

The population proportion of adults who prefer brand A is equal to 0.5.

Answer

The population proportion of adults who prefer brand A is greater than 0.5.

Answer

The population proportion of adults who prefer brand A is less than 0.5.

Question 44

A company claims that their new marketing campaign has increased the brand awareness from 40% to 60%. A sample of 400 customers shows that 240 are aware of the brand. Using a significance level of 0.05, test the company's claim.

Accepted Answer

Reject the null hypothesis.

Answer

The claim cannot be tested using a one-sample proportion test.

Answer

Fail to reject the null hypothesis.

Answer

There is not enough information to test the claim.

Question 45

A confidence interval is calculated for the proportion of students who own a smartphone. The interval is (0.7, 0.9). What is the margin of error?

Accepted Answer

0.1

Answer

0.9

Answer

0.2

Answer

0.7

Question 46

A survey finds that 30% of employees are satisfied with their job. A manager believes that the satisfaction level is higher in her department and conducts a survey in her department, which shows that 45% of the employees are satisfied. Using a sample size of 100 employees, test the manager's claim.

Accepted Answer

Reject the null hypothesis.

Answer

There is not enough information to test the claim.

Answer

The claim cannot be tested using a two-sample proportion test.

Answer

Fail to reject the null hypothesis.

Question 47

Which of the following is a key assumption of hypothesis testing for proportions?

Accepted Answer

The sample is randomly selected from the population.

Answer

The population standard deviation is known.

Answer

The data is normally distributed.

Question 48

A company wants to test if the proportion of defective products is less than 5%. They inspect 200 products and find 8 defective products. Using a significance level of 0.05, test the company's claim.

Accepted Answer

Reject the null hypothesis.

Answer

There is not enough information to test the claim.

Answer

The claim cannot be tested using a one-sample proportion test.

Answer

Fail to reject the null hypothesis.

Question 49

A researcher wants to estimate the proportion of adults who support a particular political party. They plan to collect data from a sample of 500 adults. What is the approximate margin of error at a 95% confidence level?

Accepted Answer

0.044

Answer

0.176

Answer

0.088

Answer

0.022

Question 50

When conducting hypothesis testing for proportions, what is the appropriate distribution to use when the sample size is small and the population standard deviation is unknown?

Accepted Answer

Normal distribution

Answer

Poisson distribution

Answer

Binomial distribution

Answer

Student's t-distribution

Question 51

A pharmaceutical company wants to know if their new drug reduces the risk of developing a certain disease. They conduct a clinical trial with 200 participants and observe that 50 participants develop the disease. Assuming a population proportion of 0.6, test the drug's effectiveness at a significance level of 0.05.

Accepted Answer

Reject the null hypothesis.

Answer

There is not enough information to test the claim.

Answer

Fail to reject the null hypothesis.