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SpyIntel [72]
3 years ago
10

weight per apple they ship is 120 grams with a standard deviation of 12 grams. Data generated from a sample of 49 apples randoml

y selected from a shipment indicated a mean weight of 122.5 grams per apple. Calculate and interpret a 95% confidence interval for the mean weight per apple.
Mathematics
1 answer:
astra-53 [7]3 years ago
3 0

Answer:

The 95% confidence interval for the mean weight per apple is between 119.14 and 125.86 grams per apple. This means that we are 95% sure that the true mean weight per apple for all the apples they ship is between 119.14 and 125.86 grams per apple.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1-0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.025 = 0.975, so z = 1.96

Now, find the margin of error M as such

M = z*\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.96\frac{12}{\sqrt{49}} = 3.36

The lower end of the interval is the sample mean subtracted by M. So it is 122.5 - 3.36 = 119.14 grams per apple

The upper end of the interval is the sample mean added to M. So it is 122.5 + 3.36 = 125.86 grams per apple

The 95% confidence interval for the mean weight per apple is between 119.14 and 125.86 grams per apple. This means that we are 95% sure that the true mean weight per apple for all the apples they ship is between 119.14 and 125.86 grams per apple.

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