A data set about speed dating includes \"like\" ratings of male dates made by th
ID: 3351726 • Letter: A
Question
A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are n=186, x overbarxequals=6.536.53, s=1.971.97. Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 7.00. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses?
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: > 7
Alternative hypothesis: < 7
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 0.05. 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)
S.E = 0.1444
DF = n - 1
D.F = 185
t = (x - ) / SE
t = - 3.25
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 - 3.25.
Thus the P-value in this analysis is 0.00069.
Interpret results. Since the P-value (0.00069) is less than the significance level (0.05), we cannot reject the null hypothesis.
Hence we have sufficient evidence in the favor of the claim that the population mean of such ratings is less than 7.00.
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