Answer to Question #269122 in Statistics and Probability for Kabi

Question

(a) Suppose a random sample of size nine is drawn from a normal distribution with unknown mean μ and variance = 4. The sample average of the nine observations is found to be 100.8.

(i) Find a 90% Confidence Interval (CI) for the population mean μ.

(ii) Determine the sample size that will ensure the 90% CI is within ±0.5 of the population mean μ.

(b) A coffee machine is supposed to dispense 6 oz of coffee per cup. A random sample of 30 cups has a mean of 5.9 oz per cup. Assume that the amount of coffee per cup dispensed by the machine is normally distributed with a standard deviation of 0.3 oz per cup.

(i) At the 0.01 level of significance, do the data provide sufficient evidence to conclude that the mean amount dispensed by the coffee machine is less than 6 oz per cup? Solve using the p-value approach.

(ii) If the probability of committing type II error β in part (i) is 0.1, what is the true mean amount of coffee per cup dispensed by the machine?