Question

Golden Bee Honey

Prompt: The Golden Bee Honey Company sells honey in 50-pound cans to several large food processors. Historically, the weight of the cans has been normally distributed. One of their customers complained that they were not getting the full weight they paid for. You were sent to the customer’s location to investigate. You pulled 16 cans from their last shipment and weighed them. The sample had a mean weight of 50.48 pounds with a standard deviation of 0.42 pounds.

Response Parameters

Construct a confidence interval for the mean using the sample mean, s, and n provided.

Which of the three confidence interval equations should you use? Why?

What confidence level are you using? Why?

What are limits on your confidence interval?

What do they mean statistically?

What do they mean in terms of this problem?

Was the customer justified in their complaint?

Answer 1

Answer:

Given that,

Golden Bee Honey

Prompt:

The Golden Bee Honey Company sells honey in 50-pound cans to several large food processors.

Historically, the weight of the cans has been normally distributed. One of their customers complained that they were not getting the full weight they paid for.

You were sent to the customer’s location to investigate. You pulled 16 cans from their last shipment and weighed them.

The sample had a mean weight of 50.48 pounds with a standard deviation of 0.42 pounds.

Construct a confidence interval for the mean using the sample mean, s, and n provided:

Excel add-in (MegaStat) Procedure:

Step 1: In EXCEL, Select ADD-Ins > Mega Stat > Hypothesis Tests.

Step 2: Choose Mean Vs Hypothesized Value.

Step 3: Choose Summary Input.

Step 4: Enter B1:B4 under Input Range (Select range with label mean, Sd, n).

Step 5: Enter 0 under Hypothesized mean.

Step 6: Check t-test, enter Confidence level as 99.0.  

Step 7: Choose not equal in the alternative.

Step 8: Click OK.

Output:

Hypothesis Test: Mean Vs Hypothesized Value:

0.0000	hypothesized value
50.4800	mean
0.4200	std. dev
0.1050	std. error
16	n
480.76	t
7,91E-33	p-value(two-tailed)
50.1706	Confidence interval 99% lower
50.7894	Confidence interval 99% upper
0.3094	Margin of error

From the output, the 99% confidence interval is (50.1706, 50.7894).

Which of the three confidence interval equations should you use? Why:

The three confidence interval given below,

• The 99% confidence interval is .
• The 95% confidence interval is .
• The 90% confidence interval is .

What confidence level are you using? Why:

Here, consider a 99% confidence interval for given data.

Reason:

The confidence level represents the percentage of confidence. Therefore, among the three confidence intervals, select 99%.

What are limits on your confidence interval:

From the output, the 99% confidence interval is (50.1706, 50.7894).

What do they mean statistically:

Here, the mean value is 50.48, which is lies in the range of confidence interval.

Therefore, the mean is not significant.

What do they mean in terms of this problem:

Here, the mean represents the mean weight of the honey bags.

Was the customer justified in their complaint:

Here, the justification of the customer complaint is correct because the mean weight is not significant.