Question

A company that packages salted and unsalted mixed nuts received a complaint that claimed that the company’s salted packages contain more whole cashews than their unsalted packages do. The quality control department investigated the claim by randomly selecting a sample of 45 of each type of package, counting the number of cashews in each package, and finding the mean and standard deviation for both types of packages. Which of the following are the correct null and alternative hypotheses to test the complaint’s claim, where μS is the mean number of cashews per package of salted nuts and μU is the mean number of cashews per package of unsalted nuts?

A. H₀ : µ1 - µ2 = 0; Ha : µ1 - µ2 ≠ 0.
B. H₀ : µ1 - µ2 = 0; Ha : µ1 - µ2 > 0.
C. H₀ : µ1 - µ2 < 0; Ha : µ1 - µ2 > 0.
D. H₀ : µ1 - µ2 ≠ 0; Ha : µ1 - µ2 < 0.
E. H₀ : µ1 - µ2 > 0; Ha : µ1 - µ2 = 0.

Answer 1

The null hypothesis states no difference exists between the mean number of cashews in salted and unsalted nut packages, while the alternative hypothesis posits that salted packages have more cashews on average.

Step-by-step explanation:

The correct null and alternative hypotheses to test the company's complaint of salted packages containing more whole cashews compared to unsalted packages, where μS is the mean number of cashews per package of salted nuts and μU is the mean number of cashews per package of unsalted nuts, are:

• H0: μS - μU = 0
• Ha: μS - μU > 0

The null hypothesis (H0) states that there is no difference in the mean number of cashews between the salted and unsalted packages, while the alternative hypothesis (Ha) indicates that the salted packages contain a greater number of cashews on average than the unsalted packages, which aligns with the complaint.