Question

1. A sample of 30 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.5 ounces. What is the margin of error at 95% confidence?

2. A sample of 30 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.5 ounces. What is the 95% confidence interval?

3. A sample of 30 Valencia oranges showed a mean weight of 5.5 ounces with a standard deviation of 0.5 ounces. Do Valencia oranges weigh less than 5.6 ounces? Select the correct formulation:

Answer 1

1) n =30

Sample mean =

Sample standard deviation = s = 0.5

Confidence level = c = 0.95

Here population standard deviation is not known so we use t interval.

Margin of error (e) :

where tc is t critical value for alpha = 1 - c = 1 - 0.95 = 0.05 and

degrees of freedom = n - 1 = 30 - 1 = 29

tc = 2.045 (From statistical table of t values)

e = 2.045 * 0.091287

e = 0.187 (Round to 3 decimal)

Margin of error = 0.187

2)

95% Confidence interval for population mean is

(Round to 3 decimal)

95% Confidence interval for population mean is (5.313, 5.687)

3)

Here we have to test that

95% Confidence interval for population mean is (5.313, 5.687)

Here confidence interval contains null values 5.6

So we fail to reject H0.

Conclusion : Valencia oranges do not weigh less than 5.6 ounces