Question

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 21 people reveals the mean yearly consumption to be 33 kilograms (kg) with a standard deviation of 11 kg. Assume a normal population.

a-1. What is the value of the population mean?

Population mean           (Click to select)Unknown3344

a-2. What is the best estimate of this value?

Estimate value          

b-1. Explain why we need to use the t distribution.

(Click to select)Use the t distribution as the population standard deviation is known.Use the t distribution as the population standard deviation is unknown.Use the t distribution as the population mean is known.

b-2. What assumption do you need to make?

(Click to select)We must assume that the population is normally distributed.We must assume that the population is binomially distributed.We must assume that the population is not normally distributed.

c. For a 95% confidence interval, what is the value of t? (Round the final answer to 3 decimal places.)

Value of t          

d. Develop the 95% confidence interval for the population mean. (Round the final answers to 3 decimal places.)

Confidence interval for the population mean is and .

e. Would it be reasonable to conclude that the population mean is 36 kg?

(Click to select)YesNo

That value is (Click to select)reasonablenot reasonable because it is (Click to select)not insideinside the interval.

Answer 1

We have given sample mean x bar = 33 , sample standard deviation s = 11 , n = 21 , C = 0.95

a1) Here value of population mean is not given. Hence Population mean is Unknown.

a2) We know that sample mean is best estimate of population mean. Hence the best estimate value = 33

b1) We know that when population standard deviation is unknown then we use t distribution, Hence Use the t distribution as the population standard deviation is unknown.

b2) We must assume that the population is normally distributed.

c) We have C = 0.95 hence we get = 1 - C = 0.05 and n-1 = 20

Hence by using t table we get t_0.95= 2.086

d)

e) YES

That value is reasonable because it is inside the interval.

Hope this will help you. Thank you. :)