Question

Question 1 :Moving companies are required by the government to publish a carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose Company A and Company B each decided to determine this figure by sampling their records, and they report the data shown in the table: Company A Company B Total Shipment Sampled 900 750 Number of shipment with a claim $50 162 60 Government agency would like to determine if Company A has a higher proportion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B. What is the value for the Pooled Estimator of population proportion?

Select one: A. 0.18

B. 0.08

C. 0.1345

D. 0.26

Question 2 :Moving companies are required by the government to publish a carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose Company A and Company B each decided to determine this figure by sampling their records, and they report the data shown in the table: Company A Company B Total Shipment Sampled 900 750 Number of shipment with a claim $50 162 60 At = 5%, can the government agency conclude that Company A has a higher proportion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B?

Select one:

A. Since test statistics z=5.927 > critical value z=1.645, we reject the null hypothesis. There is sufficient evidence to indicate that Company A has a higher portion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B.

B. Since test statistics z=1.645 < critical value z=5.927, we failed to reject the null hypothesis. There is sufficient evidence to indicate that Company A does not have a higher portion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B.

C. Since test statistics z=5.927 > critical value z=1.96, we reject the null hypothesis. There is sufficient evidence to indicate that Company A has a higher portion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B.

D. Since test statistics t=5.927 > critical value t=2.326, we reject the null hypothesis. There is sufficient evidence to indicate that Company A has a higher portion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B.

Answer 1

Question 1 :Moving companies are required by the government to publish a carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose Company A and Company B each decided to determine this figure by sampling their records, and they report the data shown in the table: Company A Company B Total Shipment Sampled 900 750 Number of shipment with a claim $50 162 60 Government agency would like to determine if Company A has a higher proportion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B. What is the value for the Pooled Estimator of population proportion?

Pooled Estimator of population proportion is given by,

Here in given problem,

  

  

The value for the Pooled Estimator of population proportion is 0.1345.

Question 2 :Moving companies are required by the government to publish a carrier Performance Report each year. One of the descriptive statistics they must include is the annual percentage of shipments on which a $50 or greater claim for loss or damage was filed. Suppose Company A and Company B each decided to determine this figure by sampling their records, and they report the data shown in the table: Company A Company B Total Shipment Sampled 900 750 Number of shipment with a claim $50 162 60 At = 5%, can the government agency conclude that Company A has a higher proportion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B?

Here Z test for the difference between two proportions should be used.

It is given by,

z-score at 0.05 level of significance is 1.645

Therefore since test statistics z=5.927 > critical value z=1.645, we reject the null hypothesis. There is sufficient evidence to indicate that Company A has a higher portion of shipments in which a $50 or greater claim for loss or damage is filed than does the Company B.