in one city, the average amount of time that tenth-graders spend watching televi
ID: 3229841 • Letter: I
Question
in one city, the average amount of time that tenth-graders spend watching television each week is 21.6 hours. the principal of Birchwood high school believes that at his school, tenth graders watch less television. for a sample of 28 tenth graders from Birchwood high school, the mean amount of time spent watching television per week was 19.4 hours. do the data provide sufficient evidence to conclude that for tenth graders at Birchwood high school, the mean amount of time spent watching television per week is less than the city average of 21.6 hours? perform the appropriate hypothesis test using a significance level of 15%. assume that ¤=7.2 hours.
Explanation / Answer
Solution :-
Given, = 21.6, x = 19.4, s = 7.2, significance level of 15% or 0.15
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 21.6
Alternative hypothesis: < 21.6
Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.15. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = s / sqrt(n) = 7.2 / sqrt(28) = 1.36
DF = n - 1 = 28 - 1 = 27
t = (x - ) / SE = (19.4 - 21.6)/1.36 = -1.62
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
The observed sample mean produced a t statistic test statistic of -1.62. We use the t Distribution Calculator to find P(t < -1.62) = 0.1169. Thus the P-value in this analysis is 0.1168.
Interpret results. Since the P-value (0.1169) is lesser than the significance level (0.15), we can reject the null hypothesis. Thus accepting alternate hypothesis, that the data provide sufficient evidence to conclude that for tenth graders at Birchwood high school, the mean amount of time spent watching television per week is less than the city average of 21.6 hours.
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