Question

The State Farm Insurance Company boasts that 90% of its customers who make claims are satisfied with the service. To check the accuracy of this declaration, the company conducts a survey wherein customers are asked whether they were satisfied with the quality of service. 153 were satisfied and 24 were not satisfied. Can we infer at the 5% level of significance that the satisfaction rate is less than 90%? (Use 4 decimal places in your initial work for this problem.)

1.a.Is the test statistic for this test Z or t?

1.b.What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)

1.c.What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)

1.d.What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)

1.e.

What decision should be made?

Select one:

a. Do not reject the null hypothesis

b. Can not be determined from given information

c. Reject the null hypothesis

d. Accept the null hypothesis

Answer 1

Result:

The State Farm Insurance Company boasts that 90% of its customers who make claims are satisfied with the service. To check the accuracy of this declaration, the company conducts a survey wherein customers are asked whether they were satisfied with the quality of service. 153 were satisfied and 24 were not satisfied. Can we infer at the 5% level of significance that the satisfaction rate is less than 90%? (Use 4 decimal places in your initial work for this problem.)

1.a.Is the test statistic for this test Z or t?

Z test

1.b.What is the value of the test statistic of the test? ( Enter 0 if this value cannot be determined with the given information.)

Ho: P=0.9, H₁: P<0.9

Lower tail test

p=153/177=0.8644

z = -1.5785

1.c.What is the pvalue of the test? (Enter 0 if this value cannot be determined with the given information.)

P value = 0.0572

1.d.What is the relevant bound of the rejection region? (Enter 0 if this value cannot be determined with the given information.)

Table value of z at 0.05 level = -1.645

Rejection Region: Reject Ho if z < -1.645

1.e.

What decision should be made?

Calculated z = -1.5785 , not in the rejection region

The null hypothesis is not rejected.

Select one:

a. Do not reject the null hypothesis

Z Test of Hypothesis for the Proportion
Data
Null Hypothesis            p =	0.9
Level of Significance	0.05
Number of Items of Interest	153
Sample Size	177
Intermediate Calculations
Sample Proportion	0.8644
Standard Error	0.0225
Z Test Statistic	-1.5785
Lower-Tail Test
Lower Critical Value	-1.645
p-Value	0.0572
Do not reject the null hypothesis