Question

In: Statistics and Probability

Complete the following four hypotheses, using α = 0.05 for each. The week 5 spreadsheet can...

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. Sales (Y) Calls (X1) Time (X2) Years (X3) Type
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

Solutions

Expert Solution

The hypothesis being tested is:

H0: µ = 41.5

Ha: µ > 41.5

41.500 hypothesized value
44.860 mean Sales (Y)
4.733 std. dev.
0.473 std. error
100 n
99 df
7.099 t
9.66E-11 p-value (one-tailed, upper)

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that Mean sales per week exceed 41.5 per salesperson.

The hypothesis being tested is:

H0: p = 0.55

Ha: p < 0.55

Observed Hypothesized
0.43 0.55 p (as decimal)
43/100 55/100 p (as fraction)
43. 55. X
100 100 n
0.0497 std. error
-2.41 z
.0079 p-value (one-tailed, lower)

Since the p-value (0.0079) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the Proportion of receiving online training is less than 55%.

The hypothesis being tested is:

H0: µ = 145

Ha: µ < 145

145.000 hypothesized value
152.286 mean Calls (X1)
19.038 std. dev.
3.598 std. error
28 n
27 df
2.025 t
.9736 p-value (one-tailed, lower)

Since the p-value (0.9736) is greater than the significance level (0.05), we cannot reject the null hypothesis.

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

The hypothesis being tested is:

H0: µ = 15

Ha: µ > 15

15.0000 hypothesized value
15.3880 mean Time (X2)
2.8215 std. dev.
0.2822 std. error
100 n
99 df
1.375 t
.0861 p-value (one-tailed, upper)

Since the p-value (0.0861) is greater than the significance level (0.05), we cannot reject the null hypothesis.

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

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.

orchestra answered 1 year ago
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