Question

In: Statistics and Probability

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample...

In order to determine the average weight of carry-on luggage by passengers in airplanes, a sample of 25 pieces of carry-on luggage was collected and weighed. The average weight was 21 pounds. Assume that we know the standard deviation of the population to be 5.5 pounds.

1. Calculate the Margin of Error for a 97% level of confidence for the mean weight of the carry-on luggage.

2. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.

3. Calculate the Margin of Error for a 95% level of confidence for the mean weight of the carry-on luggage.

4. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

5. Discuss why the 97% and 95% confidence intervals are different.

6. How large the sample must be in order to obtain 97% confidence interval with margin of error equal to 3.0 lb

Expert Solution

Solution: We are given:

1. Calculate the Margin of Error for a 97% level of confidence for the mean weight of the carry-on luggage

Answer: The margin of error for a 97% of confidence for the mean weight of the carry-on luggage is:

Where:

is the critical value at 0.03 significance level and can be found using the standard normal table.

Therefore, the margin of error for a 97% level of confidence for the mean weight of the carry-on luggage is

2. Determine a 97% confidence interval estimate for the mean weight of the carry-on luggage.

Answer: The 97% confidence interval estimate for the mean weight of the carry-on luggage is:

Where is the margin of error.

Therefore, the 97% confidence interval estimate for the mean weight of the carry-on luggage is:

3. Calculate the Margin of Error for a 95% level of confidence for the mean weight of the carry-on luggage.

Answer: The margin of error for a 95% of confidence for the mean weight of the carry-on luggage is:

Where:

is the critical value at 0.05 significance level and can be found using the standard normal table.

Therefore, the margin of error for a 95% level of confidence for the mean weight of the carry-on luggage is

4. Determine a 95% confidence interval estimate for the mean weight of the carry-on luggage.

Answer: The 95% confidence interval estimate for the mean weight of the carry-on luggage is:

Where is the margin of error.

Therefore, the 95% confidence interval estimate for the mean weight of the carry-on luggage is:

5. Discuss why the 97% and 95% confidence intervals are different.

Answer: The 97% and 95% cnfidence intervals are different because we used two different significance levels (0.03 for 97% and 0.05 for 95%. We know that higher the confidence level, the more wider will be confidence interval provided the other things are constant. Therefore we clearly see the 97% confidence interval is wider than the 95% confidence interval

6. How large the sample must be in order to obtain 97% confidence interval with margin of error equal to 3.0 lb

Answer: The sample size required is:

Therefore the sample required is 16.

orchestra answered 2 years ago

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