Question

10. The paper "Facebook Use and Academic Performance Among College Students: A Mixed-Methods Study with a Multi-Ethnic Sample"† describes a survey of a sample of 66 male students and a sample of 195 female students at a large university in Southern California. The authors of the paper believed that these samples were representative of male and female college students in Southern California. For the sample of males, the mean time spent per day on Facebook was 102.31 minutes. For the sample of females, the mean time was 159.61 minutes. The sample standard deviations were not given in the paper, but for purposes of this exercise, suppose that the sample standard deviations were both 115 minutes. (a) Do the data provide convincing evidence that the mean time spent on Facebook is not the same for males and for females? Test the relevant hypotheses using α = 0.05. (Use μ1 for females and μ2 for males.) State the appropriate null and alternative hypotheses. H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0 H0: μ1 − μ2 ≠ 0 Ha: μ1 − μ2 = 0 H0: μ1 − μ2 = 0 Ha: μ1 − μ2 > 0 H0: μ1 − μ2 > 0 Ha: μ1 − μ2 = 0 H0: μ1 − μ2 = 0 Ha: μ1 − μ2 ≠ 0 Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. We fail to reject H0. There is not convincing evidence that the mean time spent on Facebook is not the same for males and for females. We fail to reject H0. There is convincing evidence that the mean time spent on Facebook is not the same for males and for females. We reject H0. There is convincing evidence that the mean time spent on Facebook is not the same for males and for females. We reject H0. There is not convincing evidence that the mean time spent on Facebook is not the same for males and for females. (b) Do you think it is reasonable to generalize the conclusion from the hypothesis test in part (a) to the populations of all male college students in the United States and all female college students in the United States? Explain why you think this. This answer has not been graded yet. Need Help? Read It

Answer #1

H0: μ1 − μ2 = 0 Ha: μ1 − μ2 < 0 H0: μ1 − μ2 ≠ 0

male | Female | ||

sample mean x = | 102.310 | 159.610 | |

std deviation s= | 115.000 | 115.000 | |

sample size n= | 66 | 195 | |

std error se=s/√n= | 14.156 | 8.235 | |

degree
freedom=(se_{1}^{2}+se_{2}^{2})^{2}/(se_{1}^{2}/(n_{1}-1)+se_{2}^{2}/(n_{2}-1))= |
112 |

Point estimate =x1-x2= | -57.300 | ||

standard
error of difference
Se=√(S^{2}_{1}/n_{1}+S^{2}_{2}/n_{2})= |
16.3768 | ||

test
statistic t =(x_{1}-x_{2}-Δ_{o})/Se= |
-3.5 |

p value = 0.001

We reject H0. There is convincing evidence that the mean time
spent on Facebook is not the same for males and for females.

b)

No, since the sample has been collected from Southern California and does not represent the population ,it is not reasonable to generalize the conclusion from the hypothesis test in part (a) to the populations of all male college students in the United States and all female college students in the United States

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