Question

Each bag of different colored jelly beans is supposed to have 30% blue jelly beans. Ramon believes there are actually a greater proportion of blue jelly beans. He randomly selects 25 bags of jelly beans and finds the proportion of blue jelly beans to be 36%. He uses a significance level of alpha equals 0.1 and calculates a p-value of 0.256. What null and alternative hypothesis did Ramon use for the test, and what conclusion can he make?

Answer 1

Ramon's null hypothesis (H0) is that the proportion of blue jelly beans in each bag is 30%:H0: p = 0.30His alternative hypothesis (Ha) is that the proportion of blue jelly beans in each bag is greater than 30%:Ha: p > 0.30To test this hypothesis, Ramon uses a significance level of alpha equals 0.1, which means that he is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is true).From the sample of 25 bags of jelly beans, Ramon calculates a sample proportion of blue jelly beans of 36%. He then uses this value to calculate a test statistic and a corresponding p-value of 0.256.Since the p-value (0.256) is greater than the significance level (0.1), Ramon fails to reject the null hypothesis. This means that he does not have enough evidence to conclude that the proportion of blue jelly beans in each bag is significantly greater than 30%. It is possible that the observed difference in the sample proportion is due to random sampling variability.In other words, Ramon's conclusion is that there is not enough evidence to support his belief that there are actually a greater proportion of blue jelly beans than the specified 30%. He should not make any changes to the production or distribution process based on this sample result

Explanation: