Question

Suppose a candidate running for sheriff in a rural community claims that he will reduce the average speed of emergency response to less than 30 minutes (30 minutes is thought to be the average response time, µ = 30 with the current sheriff). Thanks to his campaign promise, he is elected sheriff and keeps careful records of response times. Since the sheriff was elected, there have been 9 emergency calls (N = 9) with a mean response time of 15 (M = 15) and a standard deviation of 3.8 (s = 3.8). Has the sheriff kept his campaign promise to reduce response time?

a)      What is the null hypothesis for this experiment?

b)      What is the alternative hypothesis for this experiment?

c)      Calculate the appropriate test statistic to test the hypothesis

d)   What is the critical value if alpha is set to .05?

e)   What is the conclusion? State in words whether we reject or fail to reject the null hypothesis and why. What does this tell us about response times under the new sheriff? Support your conclusion with the statistics you have calculated.

Answer 1

Solution :

Given that,

= 15

s = 3.8

n = 9

a.) Hypothesis:

H0 : = 30

Ha : < 30

Test Statistic:

t = ( - ) / (s /n)

t = (15 - 30 ) / ( 3.8 / 9)

t = -11.84

Degrees of freedom = df = n - 1 = 9 - 1 = 8

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,8 = 2.306

P - value = 0.00001

if P- value < 0.05 then reject H0.

P-value < 0.05, we reject H0.

there is sufficient evidence to support the claim