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.?
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 10 42 0.2381 Yes
13 50 0.26 0.062032 0.121581 0.138419 0.381581 -1.334 0.182122 9 42 0.2143 Yes
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 7 42 0.1667 Yes
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 10 42 0.2381 Yes
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 6 42 0.1429 Yes
7 50 0.14 0.049071 0.096178 0.043822 0.236178 -3.113 0.001850 8 42 0.1905 Yes
15 50 0.30 0.064807 0.127020 0.172980 0.427020 -0.741 0.458542 13 42 0.3095 Yes
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 9 42 0.2143 Yes
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 9 43 0.2093 Yes
5 50 0.10 0.042426 0.083154 0.016846 0.183154 -3.706 0.000210 9 42 0.2143 No

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.?
8 50 0.16 0.051846 0.101616 0.058384 0.261616 -2.817 0.004851 8 42 0.1905 Yes
5 50 0.10 0.042426 0.083154 0.016846 0.183154 -3.706 0.000210 7 42 0.1667 Yes
9 50 0.18 0.054332 0.106489 0.073511 0.286489 -2.520 0.011727 9 42 0.2143 Yes
6 50 0.12 0.045957 0.090073 0.029927 0.210073 -3.410 0.000650 12 42 0.2857 No
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 12 42 0.2857 Yes
10 50 0.20 0.056569 0.110872 0.089128 0.310872 -2.224 0.026165 14 42 0.3333 No
12 50 0.24 0.060399 0.118379 0.121621 0.358379 -1.631 0.102943 14 42 0.3333 Yes
14 50 0.28 0.063498 0.124454 0.155546 0.404454 -1.038 0.299387 10 42 0.2381 Yes
11 50 0.22 0.058583 0.114821 0.105179 0.334821 -1.927 0.053949 10 42 0.2381 Yes
3 50 0.06 0.033586 0.065827 -0.005827 0.125827 -4.299 0.000017 8 42 0.1905 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, 80.0% of the confidence intervals contained the true proportion of strawberry candies.