Question

A data set about speed dating includes "like" ratings of male dates made by the female dates. The summary statistics are nequals=184x overbarxequals=7.58 sequals=2.06Use a 0.05 significance level to test the claim that the population mean of such ratings is less than 8.00 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. Determine the test statistic

Answer 1

Sol:

Null Hypothesis:H0:

Alternative Hypothesis:H1:

alpha=0.05

test statistic

t=sample mean-poulation mean/samplesd/sqrt(samplesize)

=7.58-8/2.06/sqrt(184)

t=-2.77

df=n-1=184-1=183

p value is

=T.DIST.RT(2.77;183)

p=

0.003092

p<0.05

Reject Null hypothesis.

Accept alternative Hypothesis.

final conclusion that addresses the original claim

there is suffciient statistical evidence at 5% level of significance to conclude that the population mean of such ratings is less than 8.00