# Hypothesis Testing: Normal and Independent

In a one-tailed test

A. The rejection region is in one of the tails.

B. The rejection region is split between the tails.

C. The p-value is always less than the significance level.

D. The p-value is always more than the significance level.

To conduct a one sample test of means and use the z distribution as the test statistic

A. We need to know the population standard deviation.

B. We can use the sample standard deviation provided n is at least 30.

C. We need n to be at least 5.

D. Both a and b are correct.

Which of the following statements are correct when deciding whether to use the z or the t distribution

A. Use z when the sample size is 30 or more.

B. Use z when we have a normal population and know the standard deviation.

C. Use t when the population is normal, the population standard deviation is not known, and n is less than 30.

D. All of the above statements are correct.

Which of the following is not a requirement for the two-sample test of means for independent samples when both samples contain less than 30 observations?

A. Normal populations

B. Equal population standard deviations

C. Equal sample sizes

D. All of the above are required.

To conduct a test of means for two independent samples which of the following are always required?

A. At least one of the samples must have 30 observations

B. Both samples must have 30 observations

C. n and n (1 - ) must be 5.

D. None of the above.

#### Solution Preview

In a one-tailed test

A. The rejection region is in one of the tails. - correct

B. The rejection region is split between the tails. - this is a 2-tailed test

C. The p-value is always less than the significance level. -not always; the p-value is the probability of obtaining a result at least as extreme as the one that was actually observed, given that the null hypothesis is true.

D. The p-value is always more than the significance level. -not always; the p-value is the probability of obtaining a result at least as extreme as the one that was actually observed, given that the null hypothesis is true.

the answer is A

To conduct a one sample test of means and use the z distribution as ...

#### Solution Summary

This solution contains explanations regarding the theory of hypothesis testing for a normal distribution, as well as two independent samples.