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.?
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 Retain 14 55 0.2545 Yes
17 50 0.34 0.066993 0.131303 0.208697 0.471303 -0.148 0.882146 Retain 14 55 0.2545 Yes
7 50 0.14 0.049071 0.096178 0.043822 0.236178 -3.113 0.001850 Reject 12 55 0.2182 Yes
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 Retain 11 55 0.2000 Yes
6 50 0.12 0.045957 0.090073 0.029927 0.210073 -3.410 0.000650 Reject 13 55 0.2364 No
3 50 0.06 0.033586 0.065827 -0.005827 0.125827 -4.299 0.000017 Reject 9 55 0.1636 No
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 Reject 10 55 0.1818 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, 71.4% of the confidence intervals contained the true proportion of strawberry candies.