Dole Pineapple Inc. is concerned that the 16-ounce can of sliced pineapple is being overfilled. Assume the standard deviation of the process is 0.03 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? What is the decision rule?

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windyyork windyyork · Answer 1 · 2019-12-12T05:40:16+01:00

Answer: We concluded that the mean weight is greater than 16 ounces.

Step-by-step explanation:

Since we have given that

n = 50

mean = 16.05 ounces

Standard deviation = 0.03 ounce

So, hypothesis:

[tex]\mu =16\ ounces\\\\\mu>16\ ounces[/tex]

So, test statistic value would be

[tex]z=\dfrac{\bar{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{16.05-16}{\dfrac{0.03}{\sqrt{50}}}\\\\z=11.785[/tex]

At 5% level of significance, z = 1.645 in one tail test.

Since 1.645 < 11.785

Hence, we will reject the null hypothesis.

Therefore, we concluded that the mean weight is greater than 16 ounces.