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 |

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 |

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
H_{0}: 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.