Question

The research director at the Nie Pójdzie Motor Club was interested whether the annual miles driven by residents of Arkansas was greater than the 2019 average of 13,452 annual miles for a driver in the South Central region. A random sample of licensed Arkansan drivers was drawn, and a hypothesis test was performed using the .05 significance level. Some parts of the output are shown below. Please answer the following questions (a to g) using the output below. (3.5 pts.)

	AR	µ0
Mean	13962	13452
Variance	11685261
Observations	50
Pearson Correlation	#DIV/0!
Hypothesized Mean Difference	0
df	?
t Stat	1.0550
P(T<=t) one-tail	0.1483
t Critical one-tail	1.6766
P(T<=t) two-tail	0.2966
t Critical two-tail	2.0096

a) What are the degrees of freedom?

b) State the H₀ and H_a.

c) Identify the decision rule using the critical value of t (round to three decimal places).

d) Identify the decision rule using the p value method.

e) State the test statistic (t _calc)

f) What is the p value?

g) Do you reject or not reject H₀? Explain your decision using the output

Answer 1

(a) Degrees of freedom = 50 - 1 = 49

(b) H0: μ = 13452 and Ha: μ > 13452

(c) Decision rule using critical value: Reject H0, if t statistic > 1.6766 [i.e. Reject H0, if t statistic is greater than t critical value (one-tail)]

(d) Decision rule using p-value: Reject H0, if p-value is less than 0.05 significance level.

(e) Test statistic = 1.0550

(f) The p-value is 0.1483

(g) We fail to reject H0.

[Since, the test statistic is less than the t critical value or alternatively the p-value is greater than 0.05 significance level]