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Chapter 10: Q.82 (page 601)

Marketing companies have collected data implying that teenage girls use more ring tones on their cellular phones than

teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with cellular phones,

the mean number of ring tones for the girls was 3.2 with a standard deviation of 1.5. The mean for the boys was 1.7 with

a standard deviation of 0.8. Conduct a hypothesis test to determine if the means are approximately the same or if the girls’

mean is higher than the boys’ mean.

Short Answer

Expert verified

If we take α=0.05,we can see that α>ρ-value.this means we reject the null hypothesis. Thus, at the 5% significance level, there is sufficient evidence to conclude that the mean number of ringtones for girls is higher than that for boys.

Step by step solution

01

Given Information

The data is given by:

we need to test these hypotheses:

H0:μG=μβ,H1:μG>μβ

x1-X2is the difference between the mean number of ringtones for girls and boys.

We are using Student t-test for testing our hypothesis.

02

 Explanation 

SE=s12n1+s22n2=0.1445=0.38.

The test statistic is given by:

μ1μ1-μ2SE=3·9474

Finding the number degrees of freedom :

df=df=SE=SE4s14n12(n1-1)+s22n22(n2-1)=SE40.00072=28.96

Using the above formula we getp-valueis0.00023

03

Graphical representation 

following are the graph

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Most popular questions from this chapter

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U.S. population reported being of two or more races. However, the percent varies tremendously from state to state. Suppose that two random surveys are conducted. In the first random survey, out of 1,000 North Dakotans, only nine people reported being of two or more races. In the second random survey, out of 500 Nevadans, 17 people reported being of two or more races. Conduct a hypothesis test to determine if the population percents are the same for the two states or if the percent for Nevada is statistically higher than for North Dakota.

Sketch a graph of the situation. Mark the hypothesized difference and the sample difference. Shade the area corresponding to the p-value.

Use the following information to answer the next 12 exercises: The U.S. Center for Disease Control reports that the mean life expectancy was 47.6 years for whites born in 1900 and 33.0 years for nonwhites. Suppose that you randomly survey death records for people born in 1900 in a certain county. Of the 124 whites, the mean life span was 45.3 years with a standard deviation of 12.7 years. Of the 82 nonwhites, the mean life span was 34.1 years with a standard deviation of 15.6 years. Conduct a hypothesis test to see if the mean life spans in the county were the same for whites and nonwhites.

Is this a right-tailed, left-tailed, or two-tailed test?

It is thought that teenagers sleep more than adults on average. A study is done to verify this. A sample of 16 teenagers has a mean of 8.9 hours slept and a standard deviation of 1.2. A sample of 12 adults has a mean of 6.9 hours slept and a standard deviation of 0.6.

Find the p-value?

At the 1% significance level, what is your conclusion?
See all solutions

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