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: 49

b) null hypothesis : 13452

Alternative hypothesis: 13452

c) Decision using critical value: Here we observe that t statistic 1.055 is less than the t critical value 1.677, it is then concluded that the null hypothesis is not rejected.

d) Decision rule using p value: Here we observe that p= 0.1483 which is greater than 0.05, it is then concluded that the null hypothesis is not rejected.

f) Here we observe that the p value is 0.1483

g) it is concluded that the null hypothesis is not rejected. Therefore, there is not enough evidence to claim that the annual miles driven by residents of Arkansas was greater than the 2019 average of 13452 annual miles for a driver in the south central region.