Question 1

A pharmaceutical company claims that their new drug lowers blood pressure by more than 10 mmHg on average. A clinical trial is conducted, and the sample mean reduction is 12 mmHg with a known population standard deviation of 5 mmHg and a sample size of 36. Which of the following is the correct null and alternative hypothesis for this test?

Accepted Answer

$$H_0$$: \mu = 10$$; H_a$$: \mu \u003e 10$$

Question 2

A researcher is testing whether a new teaching method improves test scores. The null hypothesis is that the mean score is 75. The alternative is that the mean is greater than 75. If the researcher rejects the null hypothesis when it is actually true, what type of error has occurred?

Accepted Answer

Type I error

Question 3

A hospital administrator wants to compare the average recovery times for two different surgical procedures. The population standard deviations are unknown and are assumed to be equal. Which statistical test should be used?

Accepted Answer

Pooled T-Test

Question 4

A study compares the cholesterol levels of patients before and after a new diet. The same patients are measured twice. Which test is most appropriate?

Accepted Answer

Paired T-Test

Question 5

A sample of 200 voters is surveyed, and 120 say they support a new policy. What is the point estimate for the population proportion who support the policy?

Accepted Answer

$$\hat{p} = \frac{120}{200} = 0.6$$

Question 6

Which of the following will decrease the margin of error for a confidence interval for a population proportion, assuming all other factors remain constant?

Accepted Answer

Increasing the sample size

Question 7

A researcher wants to test if a die is fair. She rolls it 120 times and records the frequency of each face. Which statistical test should she use?

Accepted Answer

Chi-Squared Goodness of Fit Test

Question 8

Which of the following statements about the linear correlation coefficient $$r is $$TRUE?

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two variables.

Question 9

Given the regression equation $$\hat{y} = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$\hat{y} = 14$$

Question 10

A study finds $$r^2 = 0.81$ for the relationship between hours studied and exam score. What does this mean?

Accepted Answer

81% of the variation in exam scores is explained by hours studied.

Question 11

A large-sample hypothesis test for a population proportion yields a p-value of 0.03. If the significance level is $$\alpha = 0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 12

Which formula is used to calculate the test statistic for a Z-Test for a population mean when the population standard deviation $$\sigma is $$known?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\frac{\sigma}{\sqrt{n}}}$$

Question 13

A chi-squared test for independence is used to analyze the relationship between smoking status (smoker/non-smoker) and lung disease (present/absent) in a sample of 500 people. What is the null hypothesis?

Accepted Answer

Smoking status and lung disease are independent.

Question 14

Which of the following is NOT an assumption for performing a two-sample t-test for means with independent samples?

Accepted Answer

The samples are paired.

Question 15

A regression analysis yields a slope estimate of 0.5 with a standard error of 0.1. To test if the slope is significantly different from zero, what is the test statistic?

Accepted Answer

$$t = \frac{0.5}{0.1} = 5$$

Question 16

A 95% confidence interval for a population mean is calculated as (18.2, 21.8). What can you conclude about a hypothesis test with $$H_0$$: \mu = 22$$ at $$\alpha = 0.05$$?

Accepted Answer

Reject $$H_0$$ because 22 is not in the interval.

Question 17

Which of the following best describes the coefficient of determination $$r^2$$?

Accepted Answer

$$r^2 is $$the proportion of the variance in the response variable explained by the predictor variable.

Question 18

A researcher wants to know if there is an association between gender (male/female) and preference for a new product (like/dislike). Which test should be used?

Accepted Answer

Chi-Squared Test for Independence

Question 19

Which of the following is the correct formula for the margin of error for a confidence interval for a population proportion?

Accepted Answer

$$E = z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

MA 162 Modules 4-6 Study Guide: Hypothesis Testing, Proportions, Chi-Square, Regression, and ANOVA

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드