Question

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.

a) Girls' mean is the same as boys' mean.

b) Girls' mean is higher than boys' mean.

c) Girls' mean is lower than boys' mean.

d) None of these

Answer 1

To conduct a hypothesis test, use the t-test and set up the hypotheses. Compute the test statistic and compare it with the critical value. If the null hypothesis is rejected, conclude that the girls' mean is higher than the boys' mean.

Step-by-step explanation:

To conduct a hypothesis test to determine if the means are approximately the same or if the girls' mean is higher than the boys' mean, we need to perform a two-sample t-test.

1. Step 1: Set up the hypotheses:
   Null hypothesis (H0): The means are approximately the same.
   Alternative hypothesis (Ha): The girls' mean is higher than the boys' mean.
2. Step 2: Set the level of significance (α). Let's assume it as 0.05.
3. Step 3: Compute the test statistic using the formula:
   t = (mean1 - mean2) / sqrt((s1^2/n1) + (s2^2/n2))
4. Step 4: Determine the critical value using the t-distribution table or a statistical software.
5. Step 5: Compare the test statistic with the critical value.
   If the test statistic is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
6. Step 6: State the conclusion.
   If the null hypothesis is rejected, it means that there is evidence to suggest that the girls' mean is higher than the boys' mean.