A confidence interval for the population mean μ tells us which values of μ are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence.
You can use this idea to carry out a test of any null hypothesis H0: μ = μ0 starting with a confidence interval: reject H0ifμ0is outside the interval and fail to reject ifμ0is inside the interval.
The alternative hypothesis is always two-sided, Ha: μ ≠ μ0, because the confidence interval extends in both directions from x.
A 95% confidence interval leads to a test at the 5% significance level because the interval is wrong 5% of the time.
In general, confidence level C leads to a test at significance level α = 1 − C.

Step 1:
In Example 17.7, a medical director found mean blood pressure x = 126.07 for an SRS of 72 executives.
The standard deviation of the blood pressures of all executives is σ = 15.
Give a 90% confidence interval for the mean blood pressure μ of all executives.

123.16 to 128.98
122.54 to 129.46
125.63 to 126.51
124.30 to 127.84

Step 2:
Find the test statistic for testing H0: μ = 128.
Give your answer to 2 decimal places.
Fill in the blank:

Step 3:
What is the P-value for the z test for H0: μ = 128 against the two-sided alternative?
Use Table A and give your answer to 4 decimal places.
Fill in the blank:

Step 4:
Explain why the test is not significant at the 10% level.

1. Because the P-value is greater than 0.1.

2. Because the margin of error for a 90% confidence interval is less than 10% of the hypothesized mean.

3. Because the true mean falls inside the 90% confidence interval.

4. Because the hypothesized mean falls inside the 90% confidence interval.

Enter the number(s) of the choice(s) you wish to select. Separate multiple selections with commas or semicolons. Your selections:

Step 5:
Find the test statistic for testing H0: μ = 129.
Give your answer to 2 decimal places.
Fill in the blank:

Step 6:
What is the P-value for the z test for testing H0 : μ = 129 against the two-sided alternative?
Use Table A and give your answer to 3 decimal places.
Fill in the blank:

Step 7:
Explain why the test is significant at the 10% level.
1. Because the two-sided P-value is smaller than 0.1.

2. Because the one-sided P-value is smaller than 0.1.

3. Because the population mean falls outside the 90% confidence interval.

4. Because the hypothesized mean falls outside the 90% confidence interval.

Enter the number(s) of the choice(s) you wish to select. Separate multiple selections with commas or semicolons. Your selections: