Question

Jumbo eggs in Australia, on average, are supposed to weigh 68 g. Margot is in charge of a quality control test that involves weighing a sample of eggs to see if the sample mean weight is significantly different than 68 g. She takes a random sample of 25 eggs and finds a mean weight of 69 g and a sample standard deviation of 1.7 g. Use a significance level of 5%.

(A) State the appropriate null and alternative hypotheses.

(B) Compute the value of the t-statistic. (Include the formula and show all work).

(C) Compute the critical value or the p-value.

(D) State your conclusion.

Answer 1

The appropriate null and alternative hypotheses are stated. The t-statistic is computed using the given values. The critical value or p-value is calculated to make a conclusion.

Step-by-step explanation:

(A) The appropriate null and alternative hypotheses for Margot's quality control test are:

Null hypothesis (H0): The mean weight of jumbo eggs is equal to 68 g.

Alternative hypothesis (Ha): The mean weight of jumbo eggs is significantly different from 68 g.

(B) To compute the value of the t-statistic, we can use the formula:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values from the problem, the formula becomes:

t = (69 - 68) / (1.7 / sqrt(25)) = 1 / (1.7 / 5) = 1 / 0.34 = 2.94

(C) To compute the critical value or p-value, we need to determine the degrees of freedom. Since the sample size is 25, the degrees of freedom is 25 - 1 = 24. We can then look up the critical t-value for a significance level of 5% and 24 degrees of freedom in the t-distribution table. Alternatively, we can use statistical software or calculators to calculate the p-value.

(D) Based on the computed t-statistic and the critical value or p-value, we can compare them to determine the conclusion. If the computed t-statistic is greater than the critical value, or the p-value is less than the significance level, we reject the null hypothesis and conclude that the sample mean weight is significantly different from 68 g. Otherwise, we fail to reject the null hypothesis and cannot conclude a significant difference in the mean weight.