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Chapter 9: Q. 70. (page 607)

One-sided test Suppose you want to perform a test of H0: 渭=5 versus Ha: 渭<5

at the 伪=0.05 significance level. A random sample of size n=20 from the population of interest yields x炉=4.7 and sx=0.74 . 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) The sample mean 4.7is less than 5

Part b)

t=-1.8130.25<P<0.05OrP=0.04283

Step by step solution

01

Part a) Step 1: Given information

H0:渭=5H1:渭<5伪=0.05n=20x炉=4.7s=0.74

02

Part a) Step 2: Calculation

The sample mean of 4.7is less than 5,which agrees with the alternative hypothesis that the mean is less than 5,and thus the sample result provides some evidence for the alternative hypothesis.

03

Part b) Step 1: Given information

H0:渭=5H1:渭<5伪=0.05n=20x炉=4.7s=0.74

04

Part b) Step 2: Calculation

We know,

t=x炉-渭0sln

The test statistic is

t=x炉-渭0sln=4.7-50.74/20=-1.813

If the null hypothesis is true, the P-value is the probability of getting the test statistic's value or a value that is more extreme.

df=n-1=20-1=19.0.25<P<0.05

Command for Ti83/84-calculator: (-1E99,-1.813,19)which will return a P-value of 0.04283. It could replace -1E99 by any other very small negative number.

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Most popular questions from this chapter

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to 伪=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

According to the Bureau of Labor Statistics, the average age of American workers is 41.9years. The manager of a large technology company believes that the company鈥檚 employees tend to be younger, on average. So she takes a random sample of 12 employees and records their ages.

Here are the data:

27 38 32 24 30 47 42 38 27 43 37 33

a. State appropriate hypotheses for testing the manager鈥檚 belief. Be sure to define the parameter of interest.

b. State the conditions for performing a test of the hypotheses in (a), and determine whether each condition is met.

c. The P-value of the test is0.003. Interpret this value. What conclusion would you make?

Teen drivers Refer to Exercise 51.

a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the conditions for inference are met.

b. Explain why the interval in part (a) provides more information than the test in Exercise 51.

Don't argue Refer to Exercise 2. Yvonne finds that 96 of the 150 students (64%) say they rarely or never argue with friends. A significance test yields a P-value of0.0291 Interpret the P-value.

Fast connection? How long does it take for a chunk of information to travel

from one server to another and back on the Internet? According to the site

internettrafficreport.com, the average response time is 200 milliseconds (about one-fifth of a second). Researchers wonder if this claim is true, so they collect data on response times (in milliseconds) for a random sample of 14 servers in Europe. A graph of the data reveals no strong skewness or 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 95% confidence interval for the mean response time is 158.22 to 189.64

milliseconds. Based on this interval, what conclusion would you make for a test of the hypotheses in part (a) at the 5% significance level?

d. Do we have convincing evidence that the mean response time of servers in the United States is different from 200 milliseconds? Justify your answer.
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