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Chapter 9: Q. 70. (page 607)

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

at the α=0.05 significance level. A random sample of size n=20 from the population of interest yields x¯=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:μ=5H1:μ<5α=0.05n=20x¯=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:μ=5H1:μ<5α=0.05n=20x¯=4.7s=0.74

04

Part b) Step 2: Calculation

We know,

t=x¯-μ0sln

The test statistic is

t=x¯-μ0sln=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

Tests and confidence intervals The P-value for a two-sided test of the null hypothesis H0:μ=15is0.03

a. Does the 99% confidence interval for μ include 15? Why or why not?

b. Does the 95% confidence interval for μ include 15? Why or why not?

Fair coin? You want to determine if a coin is fair. So you toss it 10times and record the proportion of tosses that land “heads.” You would like to perform a test of H0:p=0.5versus Ha:p≠0.5, where p= the proportion of all tosses of the

coin that would land “heads.” Check if the conditions for performing the significance test are met.

Stating hypotheses

a. A change is made that should improve student satisfaction with the parking situation at a local high school. Before the change, 37%of students approve of the parking that's provided. The null hypothesis H0:p>0.37H0:p>0.37is tested against the alternative Ha: p=0.37Ha:p=0.37

b. A researcher suspects that the mean birth weights of babies whose mothers did not see a doctor before delivery is less than 3000 grams. The researcher states the hypotheses as

H0:x-=3000grams-5H0:x¯=3000grams

Ha: x-<3000grams Ha:x¯<3000grams

explain what's wrong with the stated hypotheses. Then give correct hypotheses.

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.

Reality TVTelevision networks rely heavily on ratings of TV shows when deciding

whether to renew a show for another season. Suppose a network has decided that

“Miniature Golf with the Stars” will only be renewed if it can be established that more than 12%of U.S. adults watch the show. A polling company asks a random sample of 2000U.S. adults if they watch “Miniature Golf with the Stars.” The network uses the data to perform a test of

H0:p=0.12

Ha:p>0.12

where pis the true proportion of all U.S. adults who watch the show. Describe a Type Ierror and a TypeIIerror in this setting, and give a possible consequence of each.
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