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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 the following is not a condition for performing a significance test about an unknown population proportion p?

(a) The data should come from a random sample or randomized experiment.

(b) Individual measurements should be independent of one another.

(c) The population distribution should be approximately Normal, unless the sample size is large.

(d) Both np and n(1 - p) should be at least 10.

(e) If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.

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