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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鈥�

mean is higher than the boys鈥� mean.

Short Answer

Expert verified

If we take 伪=0.05,we can see that 伪>蚁-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:渭G=渭尾,H1:渭G>渭尾

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:

渭1渭1-渭2SE=3路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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