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The firmness of a piece of fruit is an important indicator of fruit ripeness. The Magness-Taylor firmness was determined for one sample of 20 golden apples with a shelf life of zero days, resulting in a sample mean of 8.74 and sample standard deviation of

The firmness of a piece of fruit is an important indicator of fruit ripeness. The Magness-Taylor firmness was determined for one sample of 20 golden apples with a shelf life of zero days, resulting in a sample mean of 8.74 and sample standard deviation of 0.66, and another sample of 20 apples with a shelf life of 20 days, with a sample mean and sample standard deviation of 4.96 and 0.39, respectively.

(a) Calculate a confidence interval for the differences between the true average firmness of zero-day apples and true average firmness of 20-day apples using a confidence level of 95%. 

(b) Test with significance level 5% whether there is a difference between the true average firmness of zero-day apples and true average firmness of 20-day apples.

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