# Statistical Method for Management Questions

Question # 1.

The weights of salmon grown commercially are normally distributed with a standard deviation of

1.2 pounds and a mean weight of 7.6 pounds. A random sample of 16 fish yielded an average

weight of 7.0 pounds. At the 0.10 level of significance, is there evidence that the mean weight is

7.6 pounds? Use a p-value approach.

Question # 2.

A mail-order business prides itself in its ability to fill customers’ orders in six days or less on

average. Periodically, the operations manager selects a random sample of customer orders and

determines the number of days required to fill the orders. Based on this sample information, he

decides if the desired standard is being met. He will assume that the average number of days to fill

customers’ orders is six or less unless the data strongly suggest otherwise.

a. Establish the appropriate null and alternative hypotheses.

b. On one occasion when a sample of 40 customers was selected, the average number of days was

6.65, with a sample standard deviation of 1.5 days. Can the operations manager conclude that

his mail-order business is achieving its goal? Use a significance level of 0.025 to answer this

question.

Question # 3.

A contract with a parts supplier calls for no more than 0.04 defects in the large shipment of parts.

To test whether the shipment meets the contract, the receiving company has selected a random

sample of n = 100 parts and found 6 defects. If the hypothesis test is to be conducted using a

significance level equal to 0.05, what is the test statistic and what conclusion should the company

reach based on the sample data?

Question # 4.

US Universities found that 72% of people are concerned about the possibility that their personal

records could be stolen over the Internet. If a random sample of 300 college students at a

Midwestern university were taken and 228 of them were concerned about the possibility that their

personal records could be stolen over the Internet, could you conclude at the 0.025 level of

significance that a higher proportion of the university’s college students are concerned about

Internet theft than the public at large? Report the p-value for this test. Z0.025 = 1.96

Question # 5.

One of the major oil products companies conducted a study recently to estimate the mean gallons

of gasoline purchased by customers per visit to a gasoline station. To do this, a random sample of

customers was selected with the following data being recorded that show the gallons of gasoline

purchased. z = 1.96

Purchased 1 Purchased 2

n1 = 50 n2 = 80

1 = 34 2 = 40

x 355 x 330

Construct a 95% confidence interval estimate for the difference between two population means.

Question # 6.

A credit card company operates two customer service centers: one in Boise and one in Richmond.

Callers to the service centers dial a single number, and a computer program routes callers to the

center having the fewest calls waiting. As part of a customer service review program, the credit

card center would like to determine whether the average length of a call (not including hold time)

is different for the two centers. The managers of the customer service centers are willing to assume

that the populations of interest are normally distributed with equal variances. Suppose a random

sample of phone calls to the two centers is selected and the following results are reported:

Boise Richmond

n1 = 120 n2 = 135

35.10 s1 37.80 s2

195 x1 216 x2

Using the sample results, develop a 90% confidence interval estimate for the difference between

the two population means.

Question # 7.

Two machines are filling packages. Fifty samples from the first machine find a sample mean of

4.53 kilograms, and ninety samples from the second machine have a sample mean of 4.01

kilograms. The population standard deviation of the first machine is 0.80 kilograms, and the

population standard deviation of the second machine is 0.60 kilograms. Test the claim that the

machines are filling packages equally.

Question # 8.

A major KSA Oil company has developed two blends of gasoline. Managers are interested in

determining whether a difference in mean gasoline mileage will be obtained from using the two

blends. As part of their study, they have decided to run a test using the Chevrolet Impala

automobile with automatic transmissions. They selected a random sample of 100 Impalas using

Blend 1 and another 100 Impalas using Blend 2. Each car was first emptied of all the gasoline in

its tank and then filled with the designated blend of the new gasoline. The car was then driven 200

miles on a specified route involving both city and highway roads. The cars were then filled and

the actual miles per gallon were recorded. The following summary data were recorded:

Blend 1 Blend 2

n1 = 100 n2 = 100

s 4.0 mpg 1 s 4.2 mpg 2

x 23.4 mpg x2 25.5 mpg

Based on the sample data, using a 0.05 level of significance, what conclusion should the company

reach about whether the population mean mpg is the same or different for the two blends?

Question # 9.

A manufactured is evaluating two types of equipment for the fabrication of component. A random

sample of 50 is collected from first brand and 6 items are found to be defective. A random sample

of 80 is collected from second brand and 8 items are found to be defective.

𝒏𝟏 = 𝟓𝟎 , 𝒙𝟏 = 𝟔 , 𝒏𝟐 = 𝟖𝟎, 𝒙𝟐 = 𝟖

a. Determine if the sample sizes are large enough so that the sampling distribution for the

difference between the sample proportions is approximately normally distributed.

b. Calculate a 90% confidence interval estimate for the difference between the two population

proportions.

Question # 10.

A company conducted a survey on the launch of two types of health drinks. The first type of

healthy drink contains fruit vitamins, minerals, and antioxidants. The second contains vegetable

nutrition, potassium, dietary fiber, folate (folic acid), vitamin A, and vitamin C. A random sample

of 500 customers was asked to state their preference of the products. Of these, 230 had bought the

first type of health drink and 88% of them liked the product. The remaining had chosen the second

type and 65% of them loved it.

a. Develop a 99% confidence interval for the difference of population proportion of customers

who bought the products and liked them. Would you agree that there is a 20% difference in

customers who liked the products they bought?

b. Conduct a hypothesis testing at a 1% significance level to test whether there is a significant

difference between the two population proportions of customers who bought the products and

liked the products.

Question # 11.

A question of medical interest is whether jogging leads to a reduction in blood pressure. To learn

about this question, eight non-jogging volunteers have agreed to begin a 1-month jogging program.

At the end of the month their blood pressure were determined and compared with the earlier values,

the data in the table below. Use a significance level of 0.01 to test the hypothesis that 1-month

jogging will tend to reduce the blood pressure.

# 1 2 3 4 5 6 7 8

Blood Pressure Before 134 122 118 130 144 125 127 133

Blood Pressure After 130 120 123 127 138 121 132 134

Question # 12.

Kelly plans to go on a vacation to Las Vegas during Christmas, but the availability of rooms in the

city is a big issue between December and February due to a higher influx of tourists during that

peak season. She checks a particular motel for the number of rooms rented. She chooses 20

randomly selected dates in December and early January to examine the occupancy records for

those dates. From her collected data, she found a standard deviation of 3.86 rooms rented. If the

number of rooms rented is normally distributed, find the 95% confidence interval for the

population standard deviation of the number of rooms rented.

Question # 13.

A manager is interested in determining if the population standard deviation has dropped below

130. Based on a sample of n = 20 items selected randomly from the population, conduct the

appropriate hypothesis test at a 0.05 significance level. The sample standard deviation is 105.

Question # 14.

The manager of the Public Broadcasting System for Tennessee is considering changing from the

traditional weeklong contribution campaign to an intensive one-day campaign. In an effort to better

understand current donation patterns, she is studying past data. A staff member from a neighboring

state has speculated that male viewers’ donations have greater variability in amount than do those

of females. To test this, random samples of 25 men and 25 women were selected from people who

donated during last year’s telethon. The following statistics were computed from the sample data:

Male Female

𝑥̅1 = 12.40 𝑥̅1 = 8.92

𝑠1 = 2.50 𝑠2 = 1.34

Based on a significance level of 0.05, does it appear that male viewers’ donations have greater

variability in amount than do those of female viewers? F0.05 = 1.984

Question # 15.

As purchasing agent for the Horner-Williams Company, you have primary responsibility for securing high

quality raw materials at the best possible price. One particular material that the Horner-Williams

Company uses a great deal of is aluminum. After careful study, you have been able to reduce the

prospective vendors to two. It is unclear whether these two vendors produce aluminum that is

equally durable.

To compare durability, the recommended procedure is to put pressure on the aluminum until it

cracks. The vendor whose aluminum requires the greatest average pressure will be judged to be

the one that provides the most durable product.

For this test, 14 pieces from Vendor 1 and 14 pieces from Vendor 2 are selected at random. The

following results in pounds per square inch (psi) are noted:

Vender 1 Vender 2

n1 = 14 n2 = 14

s1 = 300 s2 = 250

Before you test the hypothesis about a difference in population means, suppose you are concerned

about whether the assumption of equal population variances is satisfied.

Based on the sample data, what would you conclude from a test at the significance level of 0.10?

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