Null And Alternative Hypotheses

HW-4

Bus 310-011

Due Date: 11:59 pm Feb 28

Total points: 16

For this assignment, submit one Excel file. Save the file Dataset_HW-4 as HW-4_Bus 310_your last name.

1. Use Part-1 sheet to answer this question.

 

A manufacturer is interested in determining whether it can claim that the boxes of detergent it sells contain, on average, more than 500 grams of detergent. The firm selects a random sample of 100 boxes and records the amount of detergent (in grams) in each box. The data are provided in the file Dataset_HW-4 sheet named Part-1.

a) Identify the null and alternative hypotheses for this situation.

b) Is there statistical support for the manufacturer’s claim? Use α = 0.10. Explain. [ For part b, reach conclusion using t-Table value and t – Test Statistic value]

c) Use the p-value to reach a statistical conclusion.

 

[1 + 3+ 2 = 6 points]

 

2. Use Part-2 sheet to answer this question.

 

A study by Hewitt Associates showed that 79% of companies offer employees flexible scheduling. Suppose a researcher believes that in accounting firms this figure is lower. The researcher randomly selects 415 accounting firms and through interviews determines that 303 of these firms have flexible scheduling. With a 1% level of significance, does the test show enough evidence to conclude that a significantly lower proportion of accounting firms offer employees flexible scheduling?

a) Identify the null and alternative hypotheses for this situation.

b) Is there statistical support for researcher’s claim? Use α = 0.01. Explain. [ For part b, reach conclusion using z-Table value and z – Test Statistic value]

c) Use the p-value to reach a statistical conclusion.

[1 + 3+ 2 = 6 points]

 

 

3. Use Part-3 sheet to answer this question.

 

As the prices of heating oil and natural gas increase, consumers become more careful about heating their homes. Researchers want to know how warm homeowners keep their houses in January and how the results from Wisconsin and Tennessee compare. The researchers randomly call 23 Wisconsin households between 7 P.M. and 9 P.M. on January 15 and ask the respondent how warm the house is according to the thermostat. The researchers then call 19 households in Tennessee the same night and ask the same question. The results follow.

 

Wisconsin	Tennessee
71	71	65	68	73	75	74	71
70	61	67	69	74	73	74	70
75	68	71	73	72	71	69	72
74	68	67	69	74	73	70	72
69	72	67	72	69	70	67
70	73	72

 

 

For α = .01, is the average temperature of a house in Tennessee significantly higher than that of a house in Wisconsin on the evening of January 15? Assume the population variances are equal and the house temperatures are normally distributed in each population. [Hint: Similar problem is available under Lec-5 folder. Use p-value generated by Excel data analysis toolpak to reach to the statistical conclusion. Make sure to formulate the null and alternative hypotheses.]

 

[4 points]