Question 1

Which of the following best describes a Type I error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 2

A researcher claims that less than 30% of adults have sleepwalked. In a random sample of 19,136 adults, 5,588 reported having sleepwalked. Test the claim at $$\alpha = 0.05. $$What is the correct null and alternative hypothesis?

Accepted Answer

$$H_0$$: p = 0.3,\ $$H_1$$: p \u003c 0.3$$

Question 3

Given a sample proportion $$\hat{p} = 0.54$$, sample size $$n = 1009$$, and claimed population proportion $$p = 0.5$$, calculate the test statistic $$z$$ for testing $$H_0$$: p = 0.5$$.

Accepted Answer

$$z = \dfrac{0.54 - 0.5}{\sqrt{(0.5)(0.5)/1009}} = 2.54$$

Question 4

Which of the following is the correct interpretation if the P-value for a hypothesis test is 0.008 and $$\alpha = 0.05$$?

Accepted Answer

Reject $$H_0$$; there is sufficient evidence to support the alternative hypothesis.

Question 5

A medical procedure is claimed to increase the probability of a baby girl ($$p \u003e 0.5). $$Which of the following describes a Type II error in this context?

Accepted Answer

Concluding the procedure is not effective when it actually is.

Question 6

Which test statistic should be used to test a claim about a population mean when the population standard deviation $$\sigma is $$unknown and $$n \u003e 30$$?

Accepted Answer

The $$t$$ statistic

Question 7

A sample of 12 adults has a mean sleep time of 6.5 hours with a standard deviation of 1.8 hours. Test the claim that the mean sleep time is less than 7 hours at $$\alpha = 0.05. $$What is the correct test statistic formula?

Accepted Answer

$$t = \dfrac{\bar{x} - \mu}{s/\sqrt{n}}$$

Question 8

If a 90% confidence interval for a population proportion $$p is$$ $$0.514 \u003c p \u003c 0.566$$, what can you conclude about the claim $$p = 0.5$$?

Accepted Answer

Reject the claim, since 0.5 is not in the interval.

Question 9

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

Accepted Answer

The probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true.

Question 10

A study tests the claim that the mean body temperature is 98.6°F. A sample of 106 adults yields a mean of 98.2°F with a standard deviation of 0.7°F. What is the test statistic for $$H_0$$: \mu = 98.6$$ using the t$-test?

Accepted Answer

$$t = \dfrac{98.2 - 98.6}{0.7/\sqrt{106}}$$

Question 11

Which of the following is NOT a requirement for using the normal approximation to test a claim about a population proportion?

Accepted Answer

The sample size $$n is $$greater than 30.

Question 12

If the significance level $$\alpha is $$set at 0.01, and the P-value for your test is 0.03, what is the correct decision?

Accepted Answer

Fail to reject $$H_0.$$

Question 13

Which of the following statements about the Student $$t$$ distribution is FALSE?

Accepted Answer

Its standard deviation is always 1.

Question 14

A hypothesis test for a population mean is performed with $$\alpha = 0.05. $$The test statistic is $$t = -6.61$$ and the critical values are $$\pm 1.983. $$What is the correct conclusion?

Accepted Answer

Reject $$H_0.$$

Question 15

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

A statement that the parameter equals a specific value.

Step-by-Step Guidance for Hypothesis Testing in Biostatistics

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