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.?
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 Reject 11 52 0.2115 Yes
12 50 0.24 0.060399 0.118379 0.121621 0.358379 -1.631 0.102943 Retain 12 52 0.2308 Yes
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 Reject 12 52 0.2308 Yes
12 50 0.24 0.060399 0.118379 0.121621 0.358379 -1.631 0.102943 Retain 12 52 0.2308 Yes
6 50 0.12 0.045957 0.090073 0.029927 0.210073 -3.410 0.000650 Reject 7 52 0.1346 Yes
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 Retain 12 52 0.2308 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.?
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 Reject 8 52 0.1538 Yes
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 Retain 10 52 0.1923 Yes
12 50 0.24 0.060399 0.118379 0.121621 0.358379 -1.631 0.102943 Retain 11 52 0.2115 Yes
21 50 0.42 0.069800 0.136805 0.283195 0.556805 1.038 0.299387 Retain 14 52 0.2692 No
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 Reject 12 52 0.2308 Yes
19 50 0.38 0.068644 0.134540 0.245460 0.514540 0.445 0.656501 Retain 14 52 0.2692 Yes
17 50 0.34 0.066993 0.131303 0.208697 0.471303 -0.148 0.882146 Retain 16 52 0.3077 Yes
15 50 0.30 0.064807 0.127020 0.172980 0.427020 -0.741 0.458542 Retain 16 52 0.3077 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, 92.9% of the confidence intervals contained the true proportion of strawberry candies.