Question

A random sample of 16 emergency reports was selected from the files of an ambulance service. The mean time (computed from the sample data) required for ambulances to reach their destinations was 13 minutes. Assume that the population of times is normally distributed with avariance of 9. Can we conclude at the 0.05 level of significance that the population mean is greater than 10 minutes? 1. Write the hypotheses, indicate the claim 2. find the critical value t-value 3. calculate the standardized t -value 4. what is the decision

Answer 1

Solution :

= 10

= 13

s = variance = 9 = 3

n = 16

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 10

H_a : > 10

= 0.05

and the critical value for a right-tailed test is t_c =1.753.

Test statistic = t

= ( - ) / s / n

= (13-10) /3 / 16

= 4

P(z >4 ) = 1 - P(z < 4) = 0.0006

P-value = 0.0006  

0.0006 < 0.05, it is concluded that the null hypothesis is rejected.

There is enough evidence to claim that the population mean μ is greater than 10, at the 0.05