An automated machine is calibrated to fill bags of pretzels so that each bag weighs 8 ounces. A worker at the factory believes the machine is not filling the bags to the correct weight. She randomly selects 40 bags of pretzels and, after weighing them, calculates the mean weight to be 8.4 ounces. Write null and alternative hypothesis to describe this situation.

Question

a. H0:p=8 Ha:p≠8
b. Ho: μ=8 Ha: μ≠8
c. H0: μ=8.4 Ha:μ≠8.4
d.H0:μ=8 Ha:μ>8

3. 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 calculator. She uses a significance level of a = 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?

a. H0:p=0..15 Ha:p>0.15
Angelina fails to reject the null hypothesis because the p-value is greater than the significance level.
b. H0: p=0.15 Ha:p<0.15
Angelina rejects the null hypothesis because the p-value is greater than the significance level.
c. H0:p=0.15 Ha:p<0.15
Angelina rejects the null hypothesis because the p-value is greater than the significance level.
d. H0:μ=0.15 Ha:μ<0.15
Angelina rejects the null hypothesis because the p-value is greater than the significance level.

4. 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 a = 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?

a. H0: p=0.36 Ha: p>0.36
Ramon fails to reject the null hypothesis because the p-value is greater than the significance level.
b. H0:p=0.3 Ha:p>0.3
Ramon fails to reject the null hypothesis because the p-value is greater than the significance level.
c. H0: p=0.3 Ha: p≠0.3
Ramon rejects the null hypothesis because the p-value is greater than the significance level.
d. H0:p=0.3 Ha:p ≠0.3
Ramon rejects the null hypothesis because the p-value is greater than the significance level.