DeVry MATH 534 Hypothesis & Confidence Interval Tests & Null Hypothesis

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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. Three individual variables. 2

1.1.       Variable 1. 2

1.2.       Variable 2. 2

1.3.       Variable 3. 2

  1. Three relationships. 2

2.1. Pair 1. 2

2.2. Pair 2. 2

2.3. Pair 3, 2

  1. Conclusion. 2

 

 

 

 

Introduction.

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

  1. Hypotheses Testing and Confidence Intervals (Calculations). 2

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

  1. Resulting table. 4
  2. Conclusions. 4

 

 

Grading Rubric

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
     

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

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

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

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

 

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.