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.?
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 9 38 0.2368 Yes
17 50 0.34 0.066993 0.131303 0.208697 0.471303 -0.148 0.882146 8 38 0.2105 Yes
13 50 0.26 0.062032 0.121581 0.138419 0.381581 -1.334 0.182122 10 38 0.2632 Yes
15 50 0.30 0.064807 0.127020 0.172980 0.427020 -0.741 0.458542 10 38 0.2632 Yes
1 50 0.02 0.019799 0.038805 -0.018805 0.058805 -4.892 0.000001 7 38 0.1842 No
7 50 0.14 0.049071 0.096178 0.043822 0.236178 -3.113 0.001850 8 38 0.2105 Yes
2 50 0.04 0.027713 0.054316 -0.014316 0.094316 -4.596 0.000004 7 38 0.1842 No
2 50 0.04 0.027713 0.054316 -0.014316 0.094316 -4.596 0.000004 3 38 0.0789 Yes
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 9 38 0.2368 Yes
6 50 0.12 0.045957 0.090073 0.029927 0.210073 -3.410 0.000650 5 38 0.1316 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.?
16 50 0.32 0.065970 0.129298 0.190702 0.449298 -0.445 0.656501 8 38 0.2105 Yes
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 6 38 0.1579 Yes
13 50 0.26 0.062032 0.121581 0.138419 0.381581 -1.334 0.182122 8 38 0.2105 Yes
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 8 38 0.2105 Yes
17 50 0.34 0.066993 0.131303 0.208697 0.471303 -0.148 0.882146 13 38 0.3421 Yes
23 50 0.46 0.070484 0.138146 0.321854 0.598146 1.631 0.102943 13 38 0.3421 Yes
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 7 38 0.1842 Yes
5 50 0.10 0.042426 0.083154 0.016846 0.183154 -3.706 0.000210 6 38 0.1579 Yes
16 50 0.32 0.065970 0.129298 0.190702 0.449298 -0.445 0.656501 13 38 0.3421 Yes
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 6 38 0.1579 Yes
4 50 0.08 0.038367 0.075197 0.004803 0.155197 -4.003 0.000063 6 38 0.1579 No

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, 85.7% of the confidence intervals contained the true proportion of strawberry candies.