# DeVry MATH 534 Hypothesis & Confidence Interval Tests & Null Hypothesis

DeVry MATH 534 Hypothesis & Confidence Interval Tests & Null Hypothesis

Complete the following four hypotheses, using α = 0.05 for each.

• 1. Mean sales per week exceed 42.5 per salesperson
• 2. Proportion receiving online training is less than 55%
• 3 Mean calls made among those with no training is at least 145
• 4. Mean time per call is 14.7 minutes

Using the same data set from part A, perform the hypothesis test for each speculation in order to see if there is evidence to support the manager’s belief. (Please see attached file)

Compute 99% confidence intervals for the variables used in each hypothesis test, and interpret these intervals.

#### Format for report:

1. Summary Report (about one paragraph on each of the four speculations)
2. Appendix with the calculations of the Eight Elements of a Test of Hypothesis, the p-values, and the confidence intervals. Include the Excel formulas or spreadsheet screen shots used in the calculations

Part A: Exploratory Data Analysis

by First Name________Last Name_________

Contents

Introduction. 2

1.1.       Variable 1. 2

1.2.       Variable 2. 2

1.3.       Variable 3. 2

2.1. Pair 1. 2

2.2. Pair 2. 2

2.3. Pair 3, 2

1-2 sentences

# 1.       Three individual variables.

## 1.1.            Variable 1

– calculations: measures of central tendency and variability

– only 1 graph: frequency distribution if Variable 1 is quantitative, qualitative chart otherwise

– 2-3 sentences of interpretation

## 1.2.            Variable 2

– the same requirements as for Variable1

## 1.3.            Variable 3

– the same requirements as for Variable1

# 2. Three relationships.

## 2.1. Pair 1(one variable is qualitative)

– graphical and numerical summary

2.2. Pair 2 (both variables are quantitative)

graphical and numerical summary

2.3. Pair 3 (both variables are variables of your choice)

graphical and numerical summary

# 3. Conclusion

2-3 sentences

Example 1.1. Unemployment in Canada. (not the project data set)

 Mean 6.846667 Median 7.050000 Mode 7.100000 Variance 6.126938 Standard Deviation 2.475265 Range 9.7000 Count (n) 60 Min 2.300000 Quartile 1 4.775000 Median 7.050000 Quartile3 8.150000 Max 12.000000 Interquartile Range (IQR) 3.375000

Unemployment in Canada: 18 years out of 60 were at the level of 7-9%%.

Example 1.2. Example for qualitative variable – vacation.(not the project data set)

 Direction Count of Direction East 82 North 37 South 37 West 81

Most of the people traveled to East and to West.

Example of 2.1. Vacation miles by gender. (not the project data set)

 Gender Sum of VacMiles Female 18897 Male 10797

Females covered more miles than males.

Example 2.2.VacMiles and FeelAway

People can feel that they are far away even if they traveled just a few miles.

Part B: Hypothesis Testing and Confidence Intervals

by First Name________Last Name_________

Using the results from Project Part A:

 Sales Calls Time Years Mean 41.89 162.1 15.226 2.23 Standard Deviation 8.3858 17.9945 2.3288 1.4060

Type of training:     Group    29.0%     None            18.0%     Online          53.0%

perform the hypothesis test for each of the following 4 hypotheses at the 0.05 level of significance. Estimate 99% confidence intervals for the variables used in each hypothesis test.

Show your calculations in section 1, fill in the table in section 2, and make conclusions in section 3.

Contents

E1. Example 1. Claim: Mean is less than 8 ounces. 2

E2. Example 2. Claim: Proportion is greater than 0.5. 3

H1. Hypothesis 1. Claim: Mean sales per week exceed 42.5 per salesperson. 4

H2. Hypothesis 2. Claim: Proportion receiving online training is less than 55%.. 4

H3. Hypothesis 3. Claim: Mean calls made among those with no training is at least 145. 4

H4. Hypothesis 4. Claim: Mean time per call is 14.7 minutes. 4

 Category Points % Description Addressing each speculation—20 points each 80 points 80% Hypothesis test, interpretation, confidence interval, and interpretation Summary report clarity 20 points 20% One paragraph on each of the speculations Total 100 points 100% A quality paper will meet or exceed all of the above requirements.

# 1.    Hypotheses Testing and Confidence Intervals (Calculations).

## E1. Example 1.Claim: Mean is less than 8 ounces.

A coffee-dispensing machine is supposed to deliver 8 ounces of liquid into each paper cup, but a consumer believes that the actual mean amount is less. The consumer obtained a sample of 16 cups of the dispensed liquid with sample mean of 7.75 ounces and variance of 0.81 ounces. Assuming that the dispensed liquid delivered per cup is normally distributed andthat α=0.05, test the consumer’s hypothesis and estimate 99% confidence interval.

Solution.

1. Hypothesis testing.

Claim: < 8. No “=” sign, so, HA=Claim:< 8. Sign “<” points to the left, so we need left-sided p-Value:

Fail to reject, so use the right column below.

HA = Claim, so use the bottom row below.

Conclusion: Not enough evidence to support the claim that < 8.

1. Confidence interval:

## E2. Example 2. Claim: Proportion is greater than 0.5.

The executives of CareFree Insurance, Inc. feel that “a majority of our employees perceive a participatory management style at CareFree.” A random sample of 200 CareFree employees is selected. Eighty employees rate the management as participatory. Test theexecutives’ hypothesis at the 0.05 level of significance and estimate 99% confidence interval.

Solution.

1. Hypothesis testing.

Claim: p>0.5. No “=” sign, so HA=Claim: p>0.5. Sign “>” points to the right, so we need right-sided test:

0

Fail to reject, so use the right column below.

HA = Claim, so use the bottom row below.

Conclusion: Not enough evidence to support the claim that > 0.5.

1. Confidence interval:
 Confidence Level 99% n 200 Number of Successes 80 OR Sample Proportion Sample Proportion 0.400000 SE 0.034641 z 2.575829 Margin of Error 0.089229 Lower Limit 0.310771 Upper Limit 0.489229

# 2.    Resulting table.

 # Claim H0 HA Test is right/left/both-tailed Reject/Fail to reject H0 Confidence interval limits lower upper E1 < 8 = 8 < 8 left fail 7.1 8.4 E2 p > 0.5 p = 0.5 p > 0.5 right fail 0.31 0.49 H1 Sales: > 42.5 H2 Online Training: p < 55% H3 Calls from salespersons w/o training ≥ 145 H4 Time per call = 14.7

# 3.    Conclusions.

E1. Not enough evidence to reject the claim that < 8.

E2.Not enough evidence to reject the claim that p > 0.5.

H1.

H2.

H3.

H4.