A survey found that 39% of 815 randomly sampled teens said that their parents ch
ID: 3269396 • Letter: A
Question
A survey found that 39% of 815 randomly sampled teens said that their parents checked to see what Web sites they visited. The following year the same question posed to 807 teens found 40% reporting such checks. Do these results provide evidence that more parents are checking?
Let p1 and p2 be the proportions of parents checking the Web sites visited in the first and second years respectively. Choose the correct null and alternative hypotheses below.
Determine the test statistic.
Find the P-value.
State the result of this hypothesis. Assume alpha equals=0.05.
Explanation / Answer
State the hypotheses: Assume p1 and p2 denote the proportions of parents checking the websites visited in the first and second year respectively. The null hypothesis is the hypothesis of no difference, which implies that there is no difference in the proportion of parents checking the websites for year 1 and 2 respectively. The researcher wants to know whether more parents are checking the website for year 2. Therefore, the hypotheses are:
H0:p1-p2=0 versus H1:p1-p2<0
Assumptions: Model: Independent random samples, level of measurement is nominal and sampling distribution is normal. For sufficiently lar ge sample size, select Z distribution as the sampling distribution. Given, alpha=0.05. Compute z test statistic to draw inference for two population proportions.
Pooled sample proportion, phatp=(x1+x2)/(n1+n2), where, x denotes number of events and n denotes number of trials, 1 and 2 are first and second year respectively.
=(318+323)/(815+807) [815*0.39=318 (rounded); 807*0.40=323 (rounded)]
=0.3952
Z=(p1hat-p2hat)/[sqrt{phatp(1-phatp)}sqrt{1/n1+1/n2}], where, phat denotes sample proportion.
=(0.39-0.40)/[{0.3952(1-0.3952)}sqrt{1/815+1/807}]
=-0.41
P value: 0.339
Rejection rule: Reject null hypothesis is P value is less than alpha=0.05. Here, P value is not less than 0.05, therefore, fail to reject null hypothesis.
Conclusion: There is insufficient sample evidence to conclude that more parents have checked the website in year 2.
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