Each bag of different colored jelly beans is supposed to have 30% blue jelly beansRamon believes there are actually a greater proportion of blue jelly beansHe 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 = 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?
Null hypothesis: The proportion of blue jelly beans in each bag is 30%.
Alternative hypothesis: The proportion of blue jelly beans in each bag is greater than 30%.
Since the p-value is greater than the significance level of alpha = 0.1, Ramon fails to reject the null hypothesis. Therefore, he does not have enough evidence to conclude that the proportion of blue jelly beans in each bag is significantly greater than 30%.
In past years, the proportion of engineering students at the local college who did not own a calculator was 0.15. Angelina believes the proportion of current population of engineering students who do not own a calculator is lower She randomly selects 55 students and finds that 6 of them do not own a calculatorShe uses a significance level of alpha = 0.05 and calculates a p-value of 0.198. What null and alternative hypothesis did Angelina use for this test, and what conclusion can she make?
Null hypothesis: The proportion of engineering students who do not own a calculator is 0.15.
Alternative hypothesis: The proportion of engineering students who do not own a calculator is less than 0.15.
Since the p-value is greater than the significance level of alpha = 0.05, Angelina fails to reject the null hypothesis. Therefore, she does not have enough evidence to conclude that the proportion of engineering students who do not own a calculator is significantly lower than 0.15.
To determine the null and alternative hypothesis for Ramon's test, we need to understand the context of his study and the question he is trying to answer. In this case, Ramon is trying to test if the actual proportion of blue jelly beans in the bags is greater than the supposed proportion of 30%.
Null hypothesis (H0): The actual proportion of blue jelly beans is equal to or less than 30%.
Alternative hypothesis (H1): The actual proportion of blue jelly beans is greater than 30%.
Ramon used a significance level (alpha) of 0.1, which means he is willing to accept a 10% chance of making a Type I error (rejecting the null hypothesis when it is actually true).
The p-value is a measure of the evidence against the null hypothesis. In this case, Ramon calculated a p-value of 0.256.
Since the p-value (0.256) is greater than the significance level (0.1), we do not have enough evidence to reject the null hypothesis. Ramon cannot conclude that there is a greater proportion of blue jelly beans in the bags based on his sample.
In other words, Ramon's data does not provide strong enough evidence to support his belief that there are more blue jelly beans than the supposed 30%.