Exercise 17.44 (below) describes a method for testing a null hypothesis by using
ID: 3152200 • Letter: E
Question
Exercise 17.44 (below) describes a method for testing a null hypothesis by using a confidence interval: A confidence interval for the population mean tells us which values of 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: = 0 starting with a confidence interval: rejectH0 if 0 is outside the interval and fail to reject if0is inside the interval. The alternative hypothesis is always two-sided, Ha: 0, 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 = 1 C. A 95% confidence interval for a population mean is 30.7 ± 3.2. Use the method described above to answer these questions.
Step 1: With a two-sided alternative, can you reject the null hypothesis that = 33 at the 5% significance level? Why?
A) No, because 33 falls in the 95% confidence interval.
B) No, because 33 falls outside the 95% confidence interval.
C) Cannot answer without knowing the P-value.
D) Yes, because 33 falls in the 95% confidence interval.
E) Yes, because 33 falls outside the 95% confidence interval.
Step 2: With a two-sided alternative, can you reject the null hypothesis that = 34 at the 5% ( = 0.05) significance level? Why?
A) No, because 34 falls in the 95% confidence interval.
B) Cannot answer without knowing the P-value for the two-sided test.
C) No, because 34 falls outside the 95% confidence interval.
D) Yes, because 34 falls in the 95% confidence interval.
E) Yes, because 34 falls outside the 95% confidence interval.
Explanation / Answer
Exercise 17.44 (below) describes a method for testing a null hypothesis by using a confidence interval: A confidence interval for the population mean tells us which values of 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: = 0 starting with a confidence interval: rejectH0 if 0 is outside the interval and fail to reject if0is inside the interval. The alternative hypothesis is always two-sided, Ha: 0, 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 = 1 C. A 95% confidence interval for a population mean is 30.7 ± 3.2. Use the method described above to answer these questions.
95% CI =(30.7-3.2, 30.7+3.2)
=(27.5, 33.9)
Step 1: With a two-sided alternative, can you reject the null hypothesis that = 33 at the 5% significance level? Why?
A) No, because 33 falls in the 95% confidence interval.
B) No, because 33 falls outside the 95% confidence interval.
C) Cannot answer without knowing the P-value.
D) Yes, because 33 falls in the 95% confidence interval.
E) Yes, because 33 falls outside the 95% confidence interval.
Step 2: With a two-sided alternative, can you reject the null hypothesis that = 34 at the 5% ( = 0.05) significance level? Why?
A) No, because 34 falls in the 95% confidence interval.
B) Cannot answer without knowing the P-value for the two-sided test.
C) No, because 34 falls outside the 95% confidence interval.
D) Yes, because 34 falls in the 95% confidence interval.
E) Yes, because 34 falls outside the 95% confidence interval.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.