Question

A medical investigation claims that the average number of infections per week at a hospital in Pennsylvania is at least 19.1. A random sample of 40 weeks had a mean number of 17.7 infections, and a sample standard deviation is 3.8. Is there enough evidence to reject the investigator’s claim? Use a 8 % level of significance to test this claim.

Answer 1

Solution :

Given that,

Population mean = = 19.1

Sample mean = = 17.7

Sample standard deviation = s = 3.8

Sample size = n = 40

Level of significance = = 0.08

This is a left (One) tailed test,

The null and alternative hypothesis is,  

Ho: 19.1

Ha: 19.1

The test statistics,

t = ( - )/ (s/)

= ( 17.7 - 19.1 ) / ( 3.8 / 40 )

= -2.33

P- Value = 0.0125   

The p-value is p = 0.0125 < 0.08, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the average number of infections per week at a hospital in Pennsylvania is at least 19.1. at the 0.08 significance level.