SCMA1000-06W16 ASSIGNMENT 2 complete solutions correct answers key

SCMA1000-06W16 ASSIGNMENT 2 complete solutions correct answers key

Topic: Confidence Interval for the population mean

1. (Modified from question #9 page 342 textbook). Please use the data set: Data for Question 1

provided in the Excel file to do this question. This data set provides the time in hours required for

35 individuals to complete their income tax returns. (8 marks)

a) Determine the sample mean and sample standard deviation (you can use Excel to

do this part). [2]

b) Let μ be the mean time required to complete an income tax return. What is the point

estimate of μ? [1]

c) Construct a 95% confidence interval for the mean time, μ, using the formula

provided in chapter 8 when the population standard deviation is unknown. Run

Excel to check your results. [3]

d) If we also constructed a 99% confidence interval for the mean time, would the 99%

confidence interval be wider or narrower than the 95% confidence interval?

Explain. [2]

Topic: Confidence Interval for the population proportion

2. A new brand of chocolate bar is being market tested. Four hundred of the new chocolate bars were

given to consumers to try. The consumers were asked whether they liked or disliked the chocolate

bar. You are given their responses below. (6 marks)

Response Frequency

Liked 300

Disliked 100

400

a) What is the point estimate for the proportion of people who liked the chocolate bar? [1]

b) Construct a 95% confidence interval for the true proportion of people who liked the chocolate

bar. [3]

c) If a new survey is going to be conducted, with 95% confidence level, how large of a sample

needs to be taken to provide a margin of error of 4% or less? (use the sample proportion as the

planning value, p*) [2]

Topic: Hypothesis Testing

3. [Modified from #51 page 411 in the textbook] A recent issue of the AARP Bulletin reported that

the average weekly pay for a woman with a high school degree is $600. Suppose you would like to

determine if the average weekly pay for all working women is significantly greater than that for

women with a high school degree. A sample of 64 working women was selected. The sample

mean is $640 and the sample standard deviation is $147. (6 marks)

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a) State the hypotheses that should be used to test whether the mean weekly pay for all

women is significantly greater than the mean weekly pay for women with a high school

degree. [1]

b) At 5% significance level, conduct a hypothesis test using the critical value approach.[3]

c) Repeat the hypothesis test using the p-value approach. [2]

Topic: Comparing two population means

4. (Modified from Case Problem 3 page 473) Please use the data set: Data for Question 4 provided

in the Excel file to do this question. This sample data set provides the annual salary for

salespersons employed in inside a local and outside the local sales position. (6 marks)

a) Use Excel (t-Test: Two-Sample Assuming Unequal Variances) to conduct a hypothesis to

determine whether there is a significant difference in the mean salary between the inside

salespersons group and the outside salespersons group. Given = 5%. [3]

(Please read the Excel Instruction part II pages 19-20 or textbook page 476)

b) Now you are going to use the information you obtained in part a) to construct a confidence

interval for the mean salary difference between the two groups using the formula we learned in

class.

Use the results obtained in the Excel outputs in part a) to fill in the table below. [3]

Inside Outside

Sample size

Sample Mean

Sample Standard Deviation

Use the information in this table and the formula we learned in chapter 9 to construct a 95%

confidence interval for the difference between the population mean salaries of the two groups (use

the number of degrees of freedom for the t distribution as the one obtained in the Excel output

from part a)). Is the result in part b) consistent with the results in part a)?

Instruction:

 You can work in a group of two on this assignment or work on your own if you prefer. If you work in a

group of two, you both should work together on every question to understand how to do each step.

 The Excel file that contains data sets for this assignment is posted on the course website. (Please click

on the Assignment 2 tab.)

 For questions using Excel, please submit your excel file or copy and paste all the Excel outputs to a

Word document to report; For questions doing by hand, clearly show your work to get the full mark

for each question.

 For all decimal results, please keep three decimal places. For money values, please keep two decimal

places.

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 You can submit your assignment at the beginning of the class on the due date or submit it online via

the Dropbox tool on the course website by 11:40 AM on the due date.