Activity 5 Data

Section 1

Sample Values Standard
Error
Margin
Error
95% Conf Interval Test
Statistic
P-value Population Values
x n p lower upper x n p C.I.?
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 8 51 0.1569 Yes
21 50 0.42 0.069800 0.136805 0.283195 0.556805 1.038 0.299387 13 51 0.2549 No
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 10 51 0.1961 Yes
5 50 0.10 0.042426 0.083154 0.016846 0.183154 -3.706 0.000210 7 51 0.1373 Yes
16 50 0.32 0.065970 0.129298 0.190702 0.449298 -0.445 0.656501 12 51 0.2353 Yes

Section 2

Sample Values Standard
Error
Margin
Error
95% Conf Interval Test
Statistic
P-value Population Values
x n p lower upper x n p C.I.?
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 9 51 0.1765 Yes
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 14 51 0.2745 Yes
6 50 0.12 0.045957 0.090073 0.029927 0.210073 -3.410 0.000650 7 51 0.1373 Yes
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 9 51 0.1765 Yes
5 50 0.10 0.042426 0.083154 0.016846 0.183154 -3.706 0.000210 10 51 0.1961 No
13 50 0.26 0.062032 0.121581 0.138419 0.381581 -1.334 0.182122 17 51 0.3333 Yes
7 50 0.14 0.049071 0.096178 0.043822 0.236178 -3.113 0.001850 11 51 0.2157 Yes
7 50 0.14 0.049071 0.096178 0.043822 0.236178 -3.113 0.001850 11 51 0.2157 Yes
13 50 0.26 0.062032 0.121581 0.138419 0.381581 -1.334 0.182122 14 51 0.2745 Yes
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 9 51 0.1765 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, 86.7% of the confidence intervals contained the true proportion of strawberry candies.