Question

Complete the following four hypotheses, using α = 0.05 for each. The week 5 spreadsheet can be used in these analyses.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. Use the Eight Steps of a Test of Hypothesis from Section 9.1 of your text book as a guide. You can use either the p-value or the critical values to draw conclusions. Be sure to explain your conclusion and interpret that to the claim in simple terms Compute 99% confidence intervals for the variables used in each hypothesis test, and interpret these intervals. Write a report about the results, distilling down the results in a way that would be understandable to someone who does not know statistics. Clear explanations and interpretations are critical. Summary Report (about one paragraph on each of the four speculations) 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. 40 144 17.4 0.00 NONE 46 145 16.8 0.00 ONLINE 37 152 19.8 0.00 NONE 47 164 15.3 0.00 ONLINE 42 135 16.1 0.00 NONE 44 169 8.9 0.00 ONLINE 52 173 18.6 0.00 ONLINE 53 184 15.2 0.00 ONLINE 49 152 22.3 0.00 ONLINE 49 166 16.2 0.00 ONLINE 45 185 13.3 1.00 ONLINE 47 157 14.3 1.00 GROUP 42 148 16.9 1.00 NONE 43 131 18.5 1.00 NONE 44 150 18.4 1.00 NONE 43 148 15.9 1.00 ONLINE 55 189 12 1.00 ONLINE 49 188 20.4 1.00 NONE 51 190 11.3 1.00 ONLINE 37 137 18.1 1.00 ONLINE 51 167 16.2 1.00 ONLINE 37 130 15.6 1.00 GROUP 37 142 18.5 1.00 NONE 46 153 14.1 1.00 ONLINE 39 149 18.8 1.00 GROUP 46 151 16 1.00 GROUP 45 158 13.9 1.00 ONLINE 46 172 12.5 1.00 ONLINE 47 188 16.3 1.00 NONE 37 148 16.2 1.00 GROUP 46 162 12.1 1.00 GROUP 52 177 14.5 1.00 ONLINE 48 175 13.7 1.00 ONLINE 40 150 10.8 1.00 GROUP 53 182 10.5 1.00 ONLINE 54 197 11.8 1.00 ONLINE 46 148 13.1 1.00 GROUP 41 153 14.7 1.00 GROUP 44 169 13.6 1.00 ONLINE 47 176 14.1 2.00 ONLINE 47 183 12.8 2.00 ONLINE 48 136 14.1 2.00 ONLINE 52 197 13.9 2.00 ONLINE 37 120 12 2.00 NONE 49 184 16.7 2.00 ONLINE 43 173 19.8 2.00 ONLINE 42 153 15.5 2.00 GROUP 37 133 19.8 2.00 NONE 42 154 14.8 2.00 ONLINE 53 178 13.2 2.00 ONLINE 45 138 18.9 2.00 NONE 42 167 18 2.00 NONE 48 171 13 2.00 GROUP 46 162 16.2 2.00 ONLINE 49 149 21.1 2.00 GROUP 48 174 18.6 2.00 GROUP 45 173 17.6 2.00 ONLINE 45 155 18.9 2.00 GROUP 44 159 18.1 2.00 ONLINE 54 174 10.8 2.00 NONE 44 139 15.2 2.00 NONE 41 158 19.3 2.00 ONLINE 43 145 18.6 2.00 NONE 47 193 13.5 2.00 ONLINE 38 145 17.1 2.00 NONE 50 184 15.6 2.00 ONLINE 41 128 15.5 2.00 NONE 45 177 14.2 2.00 GROUP 49 170 16.1 3.00 NONE 38 122 19.3 3.00 GROUP 46 171 13.6 3.00 GROUP 37 148 15.7 3.00 GROUP 42 167 17.7 3.00 ONLINE 44 148 13.5 3.00 GROUP 45 164 16.7 3.00 NONE 45 146 12 3.00 GROUP 48 177 13.9 3.00 ONLINE 49 160 13.6 3.00 GROUP 46 149 17.8 3.00 NONE 45 140 11 3.00 GROUP 45 130 20.6 3.00 GROUP 43 166 17.6 3.00 ONLINE 44 188 12.9 3.00 GROUP 41 157 11.5 3.00 ONLINE 41 155 13.6 3.00 GROUP 43 153 15.2 3.00 GROUP 37 145 18 3.00 NONE 34 133 15.2 4.00 GROUP 51 177 11.4 4.00 NONE 43 169 13.3 4.00 NONE 39 156 13.3 4.00 NONE 40 125 12.2 5.00 NONE 44 182 15.5 5.00 NONE 48 156 15.1 4.00 ONLINE 43 148 14.5 4.00 ONLINE 39 138 17.7 4.00 GROUP 42 160 10.6 4.00 NONE 54 180 11.8 5.00 GROUP 51 167 12.6 6.00 ONLINE 48 165 19.8 6.00 ONLINE

Answer 1

Mean sales per week exceeds 41.5 per salesperson

44.860	mean Sales (Y)
4.733	std. dev.
0.473	std. error
100	n
99	df
43.617	confidence interval 99.% lower
46.103	confidence interval 99.% upper
1.243	margin of error

The 99% confidence interval is between 43.617 and 46.103.

Therefore, we can conclude that mean sales per week exceed 42.5 per salesperson.

Proportion receiving online training is less than 55%

Observed
0.43	p (as decimal)
43/100	p (as fraction)
43.	X
100	n
0.05	std. error
0.3025	confidence interval 99.% lower
0.5575	confidence interval 99.% upper
0.1275	margin of error

The 99% confidence interval is between 0.3025 and 0.5575.

Therefore, we cannot conclude that the proportion receiving online training is less than 55%.

Mean calls made among those with no training is less than 145

152.286	mean Calls (X1)
19.038	std. dev.
3.598	std. error
28	n
27	df
142.317	confidence interval 99.% lower
162.254	confidence interval 99.% upper
9.968	margin of error

The 99% confidence interval is between 142.317 and 162.254.

Therefore, we cannot conclude that the Mean calls made among those with no training is less than 145.

Mean time per call is greater than 15 minutes

15.3880	mean Time (X2)
2.8215	std. dev.
0.2822	std. error
100	n
99	df
14.6470	confidence interval 99.% lower
16.1290	confidence interval 99.% upper
0.7410	margin of error

The 99% confidence interval is between 14.6470 and 16.1290.

Therefore, we cannot conclude that the Mean time per call is greater than 15 minutes.