Activity 5 Data

Section 1

Sample Values Standard
Error
Margin
Error
95% Conf Interval Test
Statistic
P-value Decision Population Values
x n p lower upper x n p C.I.?
15 50 0.30 0.064807 0.127020 0.172980 0.427020 -0.741 0.458542 Retain 13 49 0.2653 Yes
21 50 0.42 0.069800 0.136805 0.283195 0.556805 1.038 0.299387 Retain 19 49 0.3878 Yes
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 Retain 16 49 0.3265 Yes
16 50 0.32 0.065970 0.129298 0.190702 0.449298 -0.445 0.656501 Retain 14 49 0.2857 Yes
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 Reject 15 49 0.3061 No
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 Retain 15 49 0.3061 Yes
17 50 0.34 0.066993 0.131303 0.208697 0.471303 -0.148 0.882146 Retain 12 49 0.2449 Yes
20 50 0.40 0.069282 0.135790 0.264210 0.535790 0.741 0.458542 Retain 15 49 0.3061 Yes
18 50 0.36 0.067882 0.133047 0.226953 0.493047 0.148 0.882146 Retain 16 49 0.3265 Yes
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 Reject 11 49 0.2245 Yes

Section 2

Sample Values Standard
Error
Margin
Error
95% Conf Interval Test
Statistic
P-value Decision Population Values
x n p lower upper x n p C.I.?
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 Retain 14 49 0.2857 Yes
17 50 0.34 0.066993 0.131303 0.208697 0.471303 -0.148 0.882146 Retain 13 49 0.2653 Yes
15 50 0.30 0.064807 0.127020 0.172980 0.427020 -0.741 0.458542 Retain 14 49 0.2857 Yes
20 50 0.40 0.069282 0.135790 0.264210 0.535790 0.741 0.458542 Retain 13 49 0.2653 Yes
5 50 0.10 0.042426 0.083154 0.016846 0.183154 -3.706 0.000210 Reject 12 49 0.2449 No
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 Reject 16 49 0.3265 No
18 50 0.36 0.067882 0.133047 0.226953 0.493047 0.148 0.882146 Retain 17 49 0.3469 Yes

Explanation

In this activity, each group randomly selected pieces of Starburst candy from a bag and then generated a confidence interval for the true proportion of strawberry candies in the bag.

Based on previous trials, the instructor claimed that 35% of the candies were strawberry. One can check this hypothesis by seeing whether or not 35% is contained in the confidence interval. The confidence interval represents the values that are close enough to the 35% to continue believing the instructor. If the confidence interval does not contain 35%, then the results are too far away from 35% to believe the instructor's claim.

Additionally, one can conduct a hypothesis test. The null hypothesis is H0: p = 0.35. The p-value is the chance of getting the results we did if the true proportion really is 0.35. A small p-value means the results are unlikely and that the claim is probably not believable.

The last column of the table, "C.I.?", is whether or not the generated confidence interval contained the true value of the population proportion. The confidence level, 95%, is the percent of the confidence intervals should contain the true value of the population proportion. With our data, 82.4% of the confidence intervals contained the true proportion of strawberry candies.