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Chapter 9: Q. 69. (page 606)

Two-sided test Suppose you want to perform a test of H0:渭=64

versus Ha:渭notequalto64at the 伪=0.05significance level. A random sample

of size n=25 from the population of interest yields x炉=62.8 and sx=5.36

. Assume that the conditions for carrying out the test are met.

a. Explain why the sample result gives some evidence for the alternative hypothesis.

b. Calculate the standardized test statistic and P-value.

Short Answer

Expert verified

Part a) Sample mean62.8differs from64

Part b) The required answer:

t=-1.1190.20<P<0.30orP=0.2742

Step by step solution

01

Part a) Step 1: Given information

H0:渭=64Ha:渭isnotequalto64伪=0.05n=25x炉=62.8s=5.36

02

Part a) Step 2: The objective is to explain the sample result gives some evidence for carrying out the test are met 

The sample mean 62.8differs from 64,which agrees with the alternative hypothesis that the mean is not 64,and thus the sample result provides some evidence for the alternative hypothesis.

03

Part b) Step 1: Given information

H0:渭=64Ha:渭isnotequalto64伪=0.05n=25x炉=62.8s=5.36

04

Part b) Step 2: The objective is to calculate the standardized test static and P value. 

We know,

t=x炉-渭0sln

The t-test statistic is:

t=x炉-渭0s/n=62.8-645.36/25=-1.119

The P-value is the probability of receiving the test statistic's value, or a value more extreme, assuming the null hypothesis is true.

df=n-1=25-1=24

0.20=2(0.10)<P<2(0.15)=0.30

The command for the Ti83/84-calculator:

2*tcdf(-1E99,-1.119,24)which will return a P-value of 0.2742

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Most popular questions from this chapter

Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?

a. The data should come from a random sample from the population of interest.

b. Both np0and n(1-p0)should be at least 10.

c. If you are sampling without replacement from a finite population, then you should sample less than 10%of the population.

d. The population distribution should be approximately Normal unless the sample size is large.

e. All of the above are conditions for performing a significance test about a population proportion.

A95%confidence interval for the proportion of viewers of a certain reality television

show who are over 30 years old is (0.26,0.35). Suppose the show's producers want to est the hypothesis \H0:p=0.25against Ha: Ha:p鈮�0.25. Which of the following is an appropriate conclusion for them to draw at the 伪=0.05

a. Fail to reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old equals 0.25

b. Fail to reject H0there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

c. Reject H0; there is not convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from 0.25

. d. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old is greater than 0.25.

e. Reject H0; there is convincing evidence that the true proportion of viewers of this reality TV show who are over 30 years old differs from0.25.

You are thinking of conducting a one-sample ttest about a population mean 渭using a 0.05significance level. Which of the following statements is correct?

a. You should not carry out the test if the sample does not have a Normal distribution.

b. You can safely carry out the test if there are no outliers, regardless of the sample size.

c. You can carry out the test if a graph of the data shows no strong skewness, regardless of the sample size.

d. You can carry out the test only if the population standard deviation is known.

e. You can safely carry out the test if your sample size is at least 30 .

Flu vaccine Refer to ExerciseR9.5. Of the 1000 adults who were given the vaccine, 43 got the flu. Do these data provide convincing evidence to support the company鈥檚 claim?

Water! A blogger claims that U.S. adults drink an average of five 8-ounce glasses (that鈥檚 40 ounces) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no outliers.

a. State an appropriate pair of hypotheses for a significance test in this setting. Be sure to define the parameter of interest.

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

c. The 90% confidence interval for the mean daily water intake is 30.35 to 36.92 ounces. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 10% significance level?

d. Do we have convincing evidence that the amount of water U.S. children drink per day differs from 40 ounces? Justify your answer.
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