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Business Statistics

Homework 3 (110 pts)

Here is the third homework. Please submit it by the beginning of class on 06/02.

Problem 1 (6points)

A random sample of 100 credit sales in a department store showed an average sale of $120.00.

From past data, it is known that the standard deviation of the population is $40.00.

a. Determine the standard error of the mean.

b. With a 0.95 probability, determine the margin of error.

c. What is the 95% confidence interval of the population mean?

Problem 2 (6points)

The monthly incomes from a random sample of workers in a factory are shown below.

Monthly Income

(In $1,000)

4.0

5.0

7.0

4.0

6.0

6.0

7.0

9.0

a. Compute the standard error of the mean (in dollars).

b. Compute the margin of error (in dollars) at 95% confidence.

c. Compute a 95% confidence interval for the mean of the population. Assume the population has

a normal distribution. Give your answer in dollars.

Problem 3 (6points)

Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores,

26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed

the following number of students in each classification.

Freshmen 83

Sophomores 68

Juniors 85

Seniors 64

At the 5% level of significance, has there been a significant change in the classifications between

the last school year and this school year?

Problem 4 (6 points)

A random sample of 89 tourists in the Grand Bahamas showed that they spent an average of $2,860

(in a week) with a standard deviation of $126; and a sample of 64 tourists in New Province showed

that they spent an average of $2,935 (in a week) with a standard deviation of $138. At the 5% level

of significance, can we conclude if there is any significant difference between the average

expenditures of those who visited the two islands?

Problem 5 (8 points)

A carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample

of 49 past customers is taken. The average delivery time in the sample was 16.2 days. The standard

deviation of the population (σ) is known to be 5.6 days.

a. State the null and alternative hypotheses.

b. Using the critical value approach, test to determine if their advertisement is legitimate. Let α

= .05.

Problem 6 (10points)

Nancy believes that the average running time of movies is equal to 140 minutes. A sample of 4

movies was taken and the following running times were obtained. Assume the population of the

running times is normally distributed.

150 150 180 170

a. Compute the sample mean and the standard deviation.

b. State the null and alternative hypotheses.

c. Test the hypotheses at the 10% level of significance.

Problem 7 (8 points)

In a random sample of 400 employees of a local company, 180 were female.

At 95% confidence test if the proportion of females in the company is significantly less than 50%.

Write down your hypothesis and your conclusion.

Problem 8 (10 points)

In order to estimate the difference between the average daily sales of two branches of a department store, the

following data has been gathered.

Downtown Store North Mall Store Sample size n1 = 23 days n2 = 26 days

Sample mean (in $1,000) = 37 = 34

Sample standard deviation (in $1,000) S1 = 4 S2 = 5

a. Determine the point estimate of the difference between the means.

b. Determine the degrees of freedom for this interval estimation.

c. Compute the margin of error.

d. Develop a 95% confidence interval for the difference between the two population means.

Problem 9 (10 points)

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli.

Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic vs.

conventionally grown produce? State your Hypothesis and Test at  = 0.10.

Sample Size E. Coli Prevalence Organic 200 3

Conventional 500 20

Problem 10 (10 points)

In order to estimate the difference between the average Miles per Gallon of two different models of automobiles,

samples are taken and the following information is collected.

Model A Model B

Sample Size 60 55

Sample Mean 28 25

Sample Variance 16 9

a. At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon

for the two models.

b. At the 95% confidence level, test whether the average MPG performance is different or not.

Problem 11 (10 points)

The management of Recover Fast Hospital (RFH) claims that the average length of stay in their hospital after a

major surgery is less than the average length of stay at General Hospital (GH). The following data have been

accumulated to test their claim.

RFH GH Sample size 45 58

Mean (in days) 4.6 4.9

Standard Deviation () 0.5 0.6

a. Formulate the hypotheses.

b. Compute the test statistic.

c. Test to see if the average length of stay in RFH is significantly less than the average length of stay in

GH. Let  = 0.05.

Problem 12 (10 points)

In order to determine whether or not a driver's education course improves the scores on a driving exam, a

sample of 6 students were given the exam before and after taking the course. The results are shown below.

Let d = Score After - Score Before.

Student

Score

Before the Course

Score

After the Course

1 83 87

2 89 88

3 93 91

4 77 77

5 86 93

6 79 83

a. Formulate your hypothesis

b. At 95% confidence, test to see if taking the course actually increased scores on the driving exam.

Problem 13 (10 points)

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to

their fields of concentration.

Major Top Management Middle Management TOTAL

Management 280 220 500

Marketing 120 80 200

Accounting 150 150 300

TOTAL 550 450 1000

We want to determine if the position in management is independent of field (major) of concentration.

a. Formulate your hypothesis.

b. Calculate the test statistic.

c. Using the critical value approach, test the hypotheses. Let  = 0.10.