STAT 1060 Study Guide - Final Guide: Confidence Interval, Null Hypothesis, Statistical Hypothesis Testing

6. As the test statistic becomes larger, the p-value

(a) gets smaller

(b) becomes larger 

(c) stays the same, since the sample size has not been changed

(d) becomes negative.

7. To describe the sampling distribution of the sample proportion, we use

(a) The sample proportion 

(b) The population proportion 

(c) The population mean

(d) The population mean

8. When small samples are used to estimate a population mean, in cases where the population standard deviation is unknown and the original distribution is normal:

(a) There always will be a large amount of sampling error.

(b) the t-distribution must be used to obtain the critical value.

(c) the resulting margin of error for a confidence interval estimate will tend to be fairly small.

(d) the z distribution must be used to obtain the critical value.

Consider the following hypothesis test:

H0: µ = 20
Ha: µ < 20
A sample of 50 provided a sample mean of 19.4. The population standard deviation is 2.
a. Compute the value of the test statistic (to 2 decimals).

b. What is the p-value (to 3 decimals)?

c. Using a = .05, can it be concluded that the population mean is less than 20?

d. Using a = .05, what is the critical value for the test statistic?

e. State the rejection rule: Reject H0 if z is the critical value.
f. Using a = .05, can it be concluded that the population mean is less than 20

A sample of 36 observations is selected from a normal population. The sample mean is 12, and the population standard deviation is 3. Conduct the following test of hypothesis using the 0.01 significance level: H0: μ ≤ 10 H1: μ > 10

a. Is this a one- or two-tailed test?

b. What is the decision rule, Reject H0 when Z > 2.33 or when Z <= 2.33 ?

c. What is the value of the test statistic? (Round the final answer to 1 decimal place.)

d. What is your decision regarding H0? (Reject or Accept) ?

e. What is the p-value, one, zero, or close to zero ?