Question

During a period of one​ month, a random sample of 27 approved life insurance policies is​ selected, and the total processing​ time, in​ days, is recorded as shown in the data table below. Complete parts​ (a) through​ (d).

In the​ past, the mean processing time was 46 days. At the 0.05 level of​ significance, is there evidence that the mean processing time has changed from 46 ​days?

State the null and alternative hypotheses.

Determine the test statistic.
The test statistic is
​(Round to four decimal places as​ needed.)

Find the​ p-value.
​p-value =  ​(Round to four decimal places as​ needed.)

State the conclusion.
▼
Do not reject
Reject
Upper H 0. There is
▼
insufficient
sufficient
evidence to conclude that the mean processing time has changed from 46 days.

B. What assumption about the population distribution is needed in order to conduct the t test in​ (a)?
A. The population distribution is approximately uniform.
B. The population distribution is approximately normal.
C. The population distribution is skewed.

c. Construct a normal probability plot to evaluate the assumption made in​ (b). Choose the correct graph below.
A.
Normal probability plot
-2
0
2
0
100
Z value
Time (in days)

A normal probability plot has a horizontal axis labeled Z value from negative 2 to 2 in increments of 1 and a vertical axis labeled Time in days from 0 to 100 in increments of 10. Plotted points begin at the point (negative 1.2, 12) and generally forms a line that rises from left to right, ending at the point (1.2, 85). All coordinates are approximate.
B.
Normal probability plot
-2
0
2
0
100
Z value
Time (in days)

A normal probability plot has a horizontal axis labeled Z value from negative 2 to 2 in increments of 1 and a vertical axis labeled Time in days from 0 to 100 in increments of 10. Plotted points begin at the point (negative 1.8, 16) and generally forms a curve that rises from left to right at an increasing and then decreasing rate, ending at the point (1.8, 92). All coordinates are approximate.
C.
Normal probability plot
-2
0
2
0
100
Z value
Time (in days)

A normal probability plot has a horizontal axis labeled Z value from negative 2 to 2 in increments of 1 and a vertical axis labeled Time in days from 0 to 100 in increments of 10. Plotted points begin at the point (negative 1.8, 40) and generally form a horizontal line, ending at the point (1.8, 40). All coordinates are approximate.

d. Do you think that the assumption needed in order to conduct the t test in​ (a) is​ valid?
A. ​Yes, because the normal probability plot is a straight line. The population distribution is approximately normal.
B. ​No, because the normal probability plot is a straight line. The population distribution is not approximately uniform.
C. ​No, because the normal probability plot is not a straight line. The population distribution is not approximately normal.
D.​Yes, because the normal probability plot is a straight line. The population distribution is approximately uniform.

74
19
16
64
28
28
31
90
65
50
36
56
22
18
43
40
18
17
17
91
92
63
50
51
69
16
17

Answer 1

(first part)State the null and alternative hypotheses.

null hypothesis H0:$\mu$=46 and alternate hypothesis Ha:$\mu\ne46$

this is two tailed test as alternate hypothesis is two tailed

(second part)Determine the test statistic.
The test statistic is
​(Round to four decimal places as​ needed.)

test statistic t=($\bar{x}$-$\mu$)/(s/sqrt(n))=(43.7407-46)/(25.2657/sqrt(27))=-0.4647

since population standard deviation is not known/given, so we use t-test here for test of specified sample mean

(third part)Find the​ p-value.
​p-value =  ​(Round to four decimal places as​needed.)

p-value=P(|t|>-0.4647)=0.6461 ( using ms-excel=tdist(0.4647,26,2))

This is two tailed p-value as alternate hypothesis was two tailed

(fourth part) State the conclusion.

Donot reject H0 , insufficient evidence to conclude that the mean processing time has changed from 46 days.

following information has been generated using ms-excel

	x
mean($\bar{x}$)=	43.7407
sample sd=s=	25.2657
n=	27