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.
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.
For question 1, the correct answer is:
b. Ho: μ=8 Ha: μ≠8
In this hypothesis, we are comparing the population mean (μ) with a hypothesized value of 8 ounces for the bags of pretzels. The alternative hypothesis (Ha) states that the mean weight is not equal to 8, implying that the machine is not filling the bags correctly. The null hypothesis (Ho) assumes that the mean weight is equal to 8 ounces.
For question 2, the correct answer is:
c. H0: p=0.15 Ha: p<0.15
Angelina rejects the null hypothesis because the p-value is greater than the significance level.
In this hypothesis, we are comparing the population proportion (p) of engineering students who do not own a calculator to a hypothesized value of 0.15. The alternative hypothesis (Ha) states that the proportion is less than 0.15, indicating that Angelina believes the proportion has decreased. The null hypothesis (Ho) assumes that the proportion is equal to 0.15.
Since the p-value is greater than the significance level of 0.05, Angelina fails to reject the null hypothesis. This means that there is not enough evidence to support her belief that the proportion of engineering students who do not own a calculator has decreased.
For question 3, the correct answer is:
d. 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.
In this hypothesis, we are comparing the population proportion (p) of blue jelly beans to a hypothesized value of 0.3 (30%). The alternative hypothesis (Ha) states that the proportion is not equal to 0.3, suggesting that Ramon believes there is a different proportion of blue jelly beans. The null hypothesis (Ho) assumes that the proportion is equal to 0.3.
Since the p-value is greater than the significance level of 0.1, Ramon fails to reject the null hypothesis. This means that there is not enough evidence to support his belief that there is a greater proportion of blue jelly beans.