Question

The following questions are based on this information.

The scottsdale fire department aims to respond to fire calls in 4 minutes or less, on average. But, a random sample of 18 fire calls results in a sample average response of 4 minutes and 30 seconds (X¯=4.5 minutesX¯=4.5 minutes) and sample standard deviation of 1 minute (s=1 minutes=1 minute). Assume that the random variable, response times (denoted by X), is normally distributed.

Is this sufficient statistical evidence to show that the goal of the Scottsdale fire department is not being met?

Question 26

Specify the null and alternative hypotheses.

Select one:

a. H(0): μ≥4μ≥4   versus H(a): μ<4μ<4

b. H(0): μ≤4μ≤4 versus H(a): μ>4

Question 27

The standard error (SE) of X¯X¯ is

Select one:

a. 0.76

b. 0.94

c. 0.24

d. 0.06

Question 28

The test statistics value is

Select one:

a. 2.08

b. 0.66

c. 0.53

d. 8.33

Question 29

The p-value is

Select one:

a. 0.026

b. 0.301

c. 0

d. 0.019

Question 30

At α=0.05 and using the p-value

Select one:

a. We reject H(0) in favor of H(a)

b. We do not reject H(0

Answer 1

26) H(0): μ ≤ 4 versus H(a): μ > 4

27) Standard error = SE

c. SE = 0.24

28) Test statistics: Assuming normal distribution and also as the population sd is not given,we will calculate t stat.

a. t stat = 2.08

29) p value

df = 18-1 = 17

right tailed test.

using excel formula = TINV (2.08, 17,1)  = 0.026

a. p value 0.026

30) level of significance = 0.05

since p value (0.026) is less than level of significance (0.05), we reject the Null hypothesis.

a. We reject (Ho) in favor of H(a)