Marketing companies have collected data implying that teenage girls use more ring tones on their cell phones than teenage boys do. in a random sample of 20 teenage girls, the mean number of ring tones was 3.2 with a standard deviation of 1.5. in a random sample of 20 teenage boys, the mean was 2.2 ring tones, with a standard deviation of 0.8. conduct a hypothesis test to determine if the girls’ mean is higher than the boys’ mean.

The p-value here is 0.0061, which is very small and we have evidence that the girls' mean is higher than the boys' mean.

Step-by-step explanation:

We suppose that the two samples are independent and normally distributed with equal variances. Let be the mean number of ring tones for girls, and the mean number of ring tones for boys.

We want to test vs (upper-tail alternative).

The test statistic is

T =

where

.

For this case, , , , , .

and the observed value is

t = .

We can compute the p-value as P(T > 2.6309) where T has a t distribution with 20 + 20 - 2 = 38 degrees of freedom, so, the p-value is 0.0061. Because the p-value is very small, we can reject the null hypothesis for instance, at the significance level of 0.05.

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