Question

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

Answer 1

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.