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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

Based on the P-value in Exercise 31, which of the following would be the most

appropriate conclusion?

a. Because the P-value is large, we reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

b. Because the P-value is large, we fail to reject H0. We have convincing evidence that more than 50%of city residents support the tax increase.

c. Because the P-value is large, we reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

d. Because the P-value is large, we fail to reject H0. We have convincing evidence that at most 50%of city residents support the tax increase.

e. Because the P-value is large, we fail to reject H0. We do not have convincing

evidence that more than 50%of city residents support the tax increase.

Members of the city council want to know if a majority of city residents supports a 1%increase in the sales tax to fund road repairs. To investigate, they survey a random sample of 300city residents and use the results to test the following hypotheses:

H0:p=0.50

Ha:p>0.50

where pis the proportion of all city residents who support a 1% increase in the sales tax to fund road repairs.

A Type I error in the context of this study occurs if the city council

a. finds convincing evidence that a majority of residents supports the tax increase, when in reality there isn鈥檛 convincing evidence that a majority supports the increase.

b. finds convincing evidence that a majority of residents supports the tax increase, when in reality at most 50%of city residents support the increase.

c. finds convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

d. does not find convincing evidence that a majority of residents supports the tax increase, when in reality more than 50%of city residents do support the increase.

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.

Which of the following has the greatest probability?

a.P(t>2)if t has 5 degrees of freedom.

b. P(t>2) if t has 2 degrees of freedom.

c. P(z>2) if z is a standard Normal random variable.

d.P(t<2)if t has 5 degrees of freedom.

e.P(z<2) if z is a standard Normal random variable.

We want to be rich In a recent year, 73%of first-year college students responding to a national survey identified 鈥渂eing very well-off financially鈥� as an important personal goal. A state university finds that 132of an SRS of 200of its first-year students say that this goal is important. Is there convincing evidence at the 伪=0.05significance level that the proportion of all first-year students at this university who think being very well-off is important differs from the national value of 73%?
See all solutions

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