Question

A data set about speed dating includes​ "like" ratings of male dates made by the female dates. The summary statistics are

nequals=195195​,

x overbarxequals=7.537.53​,

sequals=1.971.97.

Use a

0.050.05

significance level to test the claim that the population mean of such ratings is less than

8.008.00.

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.

Answer 1

Solution :

Given that,

Population mean = = 8.00

Sample mean = = 7.53

Sample standard deviation = s = 1.97

Sample size = n = 195

Level of significance = = 0.05

The null and alternative hypothesis is,  

Ho: = 8

H1: < 8

The test statistics,

t = ( - )/ (s/)

= ( 7.53 - 8 ) / ( 1.97 /195 )

t = -3.33

n = 195

df = n-1 = 195-1 = 194

P- Value =  0.00052

The p-value is less than 0.05

Conclusion :

Reject H0, there is sufficient evidence to conclude that the mean of the population of rating is less than 8.00

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