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# Hypothesis testing with Life Trust Insurance Company

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1. Fill in the steps of the hypothesis test for the following problem. Let Population 1 be the population of convictions in Albany County.

An actuary for the Life Trust Insurance Company is responsible for adjusting automobile insurance rates based on DWI convictions. The New York State Department of Motor Vehicles provided her with the following motor conviction data for a recent year.

Albany County Queens County
Total convictions 24,384 166,197
DWI convictions 558 1,214

At the 0.01 level of significance, test the claim that the proportion of DWI (driving while intoxicated) convictions is lower in Queens County. Assume that the given data represent random samples drawn from a larger population.

(a) H0:

(b) H1:

(c) Which hypothesis is the claim? Type an X on the line segment.

H0: ______ or H1: ______

(d) CV:

(e) P-value:

(f) Be sure to define "success" for this problem.

Then, calculate values for all the variables.

TS: Show procedure for

z =

= =

= =

(g) Decision on H0:

(h) Conclusion on claim:

2. Fill in the steps of the hypothesis test for the following problem.

Let Population 1 be the population of measures of work expectation for the "preview" group.

In a study of the effect of job previews on work expectation, 60 newly hired bank tellers were given specific job previews and another group of 40 newly hired bank tellers had no previews. Their initial expectations for promotion were measured and the group with the previews had a mean of 19.14 and a standard deviation of 6.56. For the "no preview" sample group of 40 subjects, the mean is 20.81 and the standard deviation is 4.90. At the 0.10 level of significance, test the claim that the two sample groups come from populations with the same mean.

(a) H0:

(b) H1:

(c) Which hypothesis is the claim? Type an X on the line segment.

H0: ______ or H1: ______

(d) CV:

(e) P-value as an inequality from Table A-3:

(f) TS: Show procedure for t = . Fill in all values.

= = = =

(g) Decision on H0:

(h) Conclusion on claim:

3. Fill in the steps of the hypothesis test for the following problem.
Let Population 1 be the population of "before defects program."

A company training program is designed to reduce the number of defects created by employees on an assembly line for answering machines. Sample results for randomly selected employees are given below for randomly selected work days. At the 0.05 significance level, test the claim that the training program had no effect on the numbers of defects.

Employee A B C D E F G H I
Defects before program 24 24 27 19 31 29 33 20 26
Defects after program 17 22 9 12 16 21 15 15 19
Difference

(a) H0:

(b) H1:

(c) Which hypothesis is the claim? Type an X on the line segment.

H0: ______ or H1: ______

(d) CV:

(e) P-value as an inequality from Table A-3:

(f) TS: Show procedure for t = . = =
Fill in all values.

g) Decision on H0:

(h) Conclusion on claim:

4. Fill in the steps of the hypothesis test for the following problem.
Let Population 1 be the population of paint in ml from Line 1.
Assume that both populations of paint in ml, which fill the cans, are normally distributed.

The Riverside Building Supply Company uses two different lines for filling containers that are supposed to hold 3785 ml (or 1 gal) of paint. A random sample of 25 containers is obtained from the first line, while another sample of 30 containers is obtained from the second line. Both filling processes are statistically stable. The sample results are as follows:

Line 1 Line 2
= 25
= 30

= 3789 ml
= 3780 ml

= 29 ml
= 15 ml

Test the hypothesis that the first line has a larger standard deviation than the second line. Use a 0.05 level of significance.

(a) H0:

(b) H1:

(c) Which hypothesis is the claim? Type an X on the line segment.

H0: ______ or H1: ______

(d) CV from Table A-5:
[First figure the df values.]

(e) TS: Show procedure for F = =
Fill in the variances.

(f) Decision on H0:

(g) Conclusion on claim:

(h) (3) Both lines seem to be providing a mean fill amount near the desired level of 3785 ml. Describe why a smaller standard deviation would result in a higher-quality product.

##### Solution Summary

Solution provides detailed explanation, long and descriptive, about how to test hypotheses for DWI convictions.

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###### Education
• BSc , Wuhan Univ. China
• MA, Shandong Univ.
###### Recent Feedback
• "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
• "excellent work"
• "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
• "Thank you"
• "Thank you very much for your valuable time and assistance!"

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