Question 1

Suppose the heights of adult women in a city are normally distributed with a mean of 65 inches and a standard deviation of 3 inches. What is the probability that a randomly selected woman is taller than 68 inches? (Round your answer to four decimal places.)

Accepted Answer

$$0.0668$$

Question 2

A researcher wants to estimate the mean cholesterol level in a population. The population standard deviation is known to be $$\sigma = 15 mg/dL. $$What is the minimum sample size required to estimate the mean within $$\pm 3 mg/dL $$with $$95\%$$ confidence?

Accepted Answer

$$n = 97$$

Question 3

Which of the following statements about the standard normal distribution is TRUE?

Accepted Answer

The mean is $$0$$ and the standard deviation is $$1.$$

Question 4

A sample of $$n = 36$$ has a sample mean of $$\bar{x} = 80$$ and a known population standard deviation $$\sigma = 12. $$What is the $$95\%$$ confidence interval for the population mean $$\mu$$?

Accepted Answer

$$(76.08, 83.92)$$

Question 5

If the area to the left of $$z is$$ $$0.9750$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.96$$

Question 6

A pharmaceutical company claims that their new drug lowers blood pressure by more than $$10$$ mmHg on average. A sample of $$n = 24$$ patients shows a mean decrease of $$12$$ mmHg with a known standard deviation of $$4$$ mmHg. What is the $$p-$$value for testing $$H_0$$: \mu = 10$$ vs H_a$$: \mu \u003e 10$$?

Accepted Answer

$$p = 0.0017$$

Question 7

Which of the following is NOT an assumption for constructing a confidence interval for a population mean when $$\sigma is $$known?

Accepted Answer

The sample mean equals the population mean.

Question 8

A poll finds that $$60\% of a $$random sample of $$400$$ voters support a new policy. What is the $$95\%$$ confidence interval for the true proportion of voters who support the policy?

Accepted Answer

$$(0.555, 0.645)$$

Question 9

In hypothesis testing, what does the $$p-$$value represent?

Accepted Answer

The probability of obtaining a result as extreme or more extreme than the observed, assuming the null hypothesis is true.

Question 10

A manufacturer claims that the mean lifetime of their light bulbs is at least $$1200$$ hours. A sample of $$n = 50$$ bulbs has a mean of $$1180$$ hours and a known standard deviation of $$60$$ hours. What is the test statistic for testing $$H_0$$: \mu = 1200$$ vs H_a$$: \mu \u003c 1200$$?

Accepted Answer

$$z = -2.36$$

Question 11

Which of the following best describes the margin of error in a confidence interval for a population mean?

Accepted Answer

It is the maximum expected difference between the sample statistic and the true population parameter at a given confidence level.

Question 12

A hospital administrator wants to estimate the average length of stay for patients. If the standard deviation is $$\sigma = 5$$ days and the desired margin of error is $$1$$ day at $$95\%$$ confidence, what sample size is needed?

Accepted Answer

$$n = 96$$

Question 13

A $$z-$$score of $$-1.5$$ corresponds to what percentile in the standard normal distribution?

Accepted Answer

$$13.36\%$$

Question 14

Which of the following is a correct interpretation of a $$95\%$$ confidence interval for a population mean?

Accepted Answer

If we took many samples, about $$95\% of $$the intervals would contain the population mean.

Question 15

A company wants to test if the mean weight of their cereal boxes is different from $$500$$ grams. A sample of $$n = 40$$ boxes has a mean of $$495$$ grams and a known standard deviation of $$10$$ grams. What is the $$z-$$test statistic?

Accepted Answer

$$z = -3.16$$

Question 16

Which of the following is TRUE about the relationship between sample size and margin of error in confidence intervals?

Accepted Answer

As sample size increases, the margin of error decreases.

Question 17

A clinical trial tests whether a new medication changes the mean recovery time from an illness. The null hypothesis is $$H_0$$: \mu = 14$$ days. The sample mean is 12$ days, n = 16$, and $$\sigma = 4$$ days. What is the z$-test statistic?

Accepted Answer

$$z = -2.00$$

Question 18

Which of the following is a correct way to use the normalcdf function on a calculator to find $$P(1 \u003c Z \u003c 2)$$ for the standard normal distribution?

Accepted Answer

normalcdf$$(1, 2, 0, 1)$$

Question 19

A $$p-$$value is found to be $$0.03 in a $$hypothesis test with $$\alpha = 0.05. $$What is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Exam Study Guide: Sampling Distributions, Confidence Intervals, and Hypothesis Testing

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