Q: A researcher wants to test the claim that convicted burglars spend an average of $$18.7$$ months in jail. She takes a random sample of $$11$$ cases and finds $$\bar{x} = 21.3$$ months, $$s = 7.7$$ months. What are the correct null and alternative hypotheses for this test?

$$H_0$$: \mu = 18.7$$, H_a$$: \mu \neq 18.7$$

Question 1

You wish to test the claim that $$\mu \u003e 28 at a $$significance level of $$\alpha = 0.05. $$Given $$n = 50$$, $$\bar{x} = 28.3$$, and $$\sigma = 1.2$$, what is the value of the test statistic (rounded to two decimal places)?

Accepted Answer

$$2.31$$

Question 2

A researcher collects forced vital capacity data (in liters) from 15 asthmatic patients. The sample mean is $$\bar{x} = 4.01$$ liters and the population standard deviation is $$\sigma = 0.6$$ liters. What is the 95.44% confidence interval for the mean forced vital capacity for all asthmatics?

Accepted Answer

$$3.70 to$$ $$4.32$$ liters

Question 3

A researcher wants to test the claim that convicted burglars spend an average of $$18.7$$ months in jail. She takes a random sample of $$11$$ cases and finds $$\bar{x} = 21.3$$ months, $$s = 7.7$$ months. What are the correct null and alternative hypotheses for this test?

Accepted Answer

$$H_0$$: \mu = 18.7$$, H_a$$: \mu 
eq 18.7$$

Question 4

Given a sample of $$54$$ employees with a mean weight of $$183.9 lb $$and a known population standard deviation $$\sigma = 121.2 lb$$, test the claim at $$\alpha = 0.10$$ that the population mean weight is less than $$200 lb. $$What is the correct test statistic?

Accepted Answer

$$-0.93$$

Question 5

Which of the following best describes the meaning of a 95.44% confidence interval for a population mean?

Accepted Answer

If we were to take many samples and build a confidence interval from each, about 95.44% of those intervals would contain the true population mean.

Question 6

A hospital administrator wants to estimate the average length of stay for patients. If the sample mean is $$5.2$$ days, the population standard deviation is $$1.8$$ days, and the sample size is $$36$$, what is the 99% confidence interval for the mean length of stay?

Accepted Answer

$$4.7 to$$ $$5.7$$ days

Question 7

In hypothesis testing, what does the significance level $$\alpha$$ represent?

Accepted Answer

The probability of rejecting the null hypothesis when it is true.

Question 8

A pharmaceutical company claims that its new drug reduces recovery time to less than $$7$$ days. A sample of $$25$$ patients has a mean recovery time of $$6.5$$ days and a standard deviation of $$1.2$$ days. What is the correct test statistic to test the company's claim?

Accepted Answer

$$-2.08$$

Question 9

Which of the following is a correct interpretation of a P-value in hypothesis testing?

Accepted Answer

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

Question 10

A nutritionist wants to test if the average sodium content in a brand of soup is different from $$500 mg. A $$sample of $$16$$ cans has a mean of $$520 mg $$and a standard deviation of $$40 mg. $$What is the value of the test statistic?

Accepted Answer

$$2.00$$

Question 11

Which of the following statements is true regarding the use of the critical value method in hypothesis testing?

Accepted Answer

The test statistic is compared to the critical value to decide whether to reject the null hypothesis.

Question 12

A sample of $$20$$ batteries has a mean life of $$102$$ hours with a standard deviation of $$8$$ hours. The manufacturer claims the mean life is $$100$$ hours. What is the test statistic for testing the manufacturer's claim?

Accepted Answer

$$1.12$$

Question 13

If a hypothesis test results in a P-value of $$0.03$$ and the significance level is $$0.05$$, what is the correct conclusion?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following is NOT an assumption for constructing a confidence interval for a population mean when the population standard deviation is known?

Accepted Answer

The population standard deviation is unknown.

Question 15

A sample of $$36$$ students has a mean test score of $$82$$ with a population standard deviation of $$12. $$What is the 90% confidence interval for the population mean?

Accepted Answer

$$79.1 to$$ $$84.9$$

Question 16

A researcher is testing $$H_0$$: \mu = 50$$ versus H_a$$: \mu \u003e 50$$ with $$\alpha = 0.01$$. The sample mean is 53$, the population standard deviation is 6$, and the sample size is 25$. What is the critical value for this test?

Accepted Answer

$$2.33$$

Step-by-Step Guidance for Statistics Hypothesis Testing and Confidence Intervals

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