Answer to Question #210019 in Statistics and Probability for mafi

Question

A medical investigation claims that the average number of infections per week

at a hospital is 16.3. A random sample of 10 weeks had a mean number of 17.7

infections. The sample standard deviation is 1.8. Is there enough evidence to

reject the investigator’s claim at α = 0.05? Assume the variable is normally

distributed.

Answer 1

This is a one-sample t-test.

$H_0:\mu=16.3.$

$H_a:\mu\ne 16.3.$

Test statistic: $t=\frac{17.7-16.3}{\frac{1.8}{\sqrt{10}}}=2.46.$

P-value: $p=2P(T>2.46)=0.0362.$

Since the p-value is less than 0.05, reject the null hypothesis.

There is enough evidence to reject the investigator’s claim at α = 0.05.