Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is .03 ounce. The quality-control department took a random sample of 50 cans and found that the arithmetic mean weight was 16.05 ounces. At the 5% level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p-value.

Answer:

The calculated value Z = 11.792 >1.96 at a 0.05 level of significance.

The null hypothesis is rejected

The alternative hypothesis is accepted at a 0.05 level of significance.

The mean weight is less than 16 ounces

Step-by-step explanation:

Step:-1

Given that the mean of the Population = 16

Given that the standard deviation of the process

                                         σ = 0.03 ounce

Given that the mean of the sample = 16.05 ounces

Null hypothesis: H₀:μ > 16 ounces

Alternative HypothesisH₁: μ <16 ounces

Step:-2

Test statistic

              [tex]Z = \frac{x^{-} -mean}{\frac{S.D}{\sqrt{n} } }[/tex]

             [tex]Z = \frac{16.05 -16}{\frac{0.03}{\sqrt{50} } }[/tex]

            Z =  11.792

Level of significance = 0.05

Z₀.₀₅ = 1.96

Final answer:-

The calculated value Z = 11.792 >1.96 at a 0.05 level of significance.

The null hypothesis is rejected

The alternative hypothesis is accepted at a 0.05 level of significance.

The mean weight is less than 16 ounces

Data show that men who are married, and also divorced or widowed men, earn quite a bit more than men the same age who have never been married. This does not mean that a man can raise his income by getting married because men who have never been married are different from married men in many ways other than marital status. Suggest one possible lurking variable that might help explain the association between marital status and income.
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D. Married, widowed, or divorced men tend to be more committed as well as men with high income jobs. From this, we may safely conclude that getting married leads to a high income job.

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