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Chapter 9: Q 83. (page 608)

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:渭=10is0.06

a. Does the 95% confidence interval for 渭 include 10? Why or why not?

b. Does the 90% confidence interval for 渭 include 10? Why or why not?

Short Answer

Expert verified

Part (a) Yes.

Part (b) No.

Step by step solution

01

Part (a) Step 1: Given information

H0:渭=10H1:渭鈮�10P=0.06
02

Part (a) Step 2: Explanation

If the P-value is lesser than the significance level then the null hypothesis is rejected.

P=0.06>0.05=5%鈬�FailtorejectH0

A significance test at the 5% significance level is associated with a 95 percent confidence interval.

The 95 percent confidence interval comprises the value given in the null hypothesis 10 because the null hypothesis failed to reject at the 5% significance level.

03

Part (b) Step 1: Explanation

The null hypothesis is rejected if theP-value is less than the significance level.

P=0.06<0.10=10%鈬�RejectH0

A significance test at the 10% significance level is associated with a 90 percent confidence interval.

The 95 percent confidence interval does not have the value specified in the null hypothesis 10 since the null hypothesis was rejected at the 10% significance level.

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Most popular questions from this chapter

Battery life A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day鈥檚 production and tests the fully charged batteries by playing a video repeatedly until the battery dies. The quality control department will discard the batteries from that day鈥檚 production run if they find convincing evidence that the mean battery life is less than 10.5 hours. Here are a dot plot and summary statistics of the data from one day:

a. State appropriate hypotheses for the quality-control department to test. Be sure to define your parameter.

b. Check if the conditions for performing the test in part (a) are met.

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at 伪=0.05significance level and gets a P-value of 0.22

The student writes: 鈥淏ecause the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

Pressing pills Refer to Exercise 77.

a. Construct and interpret a 95% confidence interval for the true hardness 渭 of the tablets in this batch. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) is consistent with the result of the test in Exercise 77.

Potato chips A company that makes potato chips requires each shipment of

potatoes to meet certain quality standards. If the company finds convincing evidence that more than 8%of the potatoes in the shipment have 鈥渂lemishes,鈥� the truck will be sent back to the supplier to get another load of potatoes. Otherwise, the entire truckload will be used to make potato chips. To make the decision, a supervisor will inspect a random sample of potatoes from the shipment. He will then perform a test of H0:p=0.08versus Ha:p>0.08, where p is the true proportion of potatoes with blemishes in a given truckload. The power of the test to detect that p=0.11, based on a random sample of 500 potatoes and significance level 伪=0.05, is 0.764Interpret this value.

pg559炉

No homework Refer to Exercises 1 and 9. What conclusion would you make at the伪=0.05伪=0.05level?
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