The Sugar Producers Association wants to estimate the mean yearly sugar consumpt

Question

The Sugar Producers Association wants to estimate the mean yearly sugar consumption. A sample of 27 people reveals the mean yearly consumption to be 34 kilograms (kg) with a standard deviation of 12 kg. Assume a normal population. a-1. What is the value of the population mean? Population mean (Click to select) 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) b-2. What assumption do you need to make? (Click to select) C. For a 98% confidence interval, what is the value of t? (Round the final answer to 3 decimal places.) Value of t d. Develop the 98% confidence interval for the population mean. (Round the final answers to 3 decimal places.) Confidence interval for the population mean is e. Would it be reasonable to conclude that the population mean is 36 kg? (Click to select) That value is (Click to select)+ because it is (Click to select) the interval.

Explanation / Answer

Answers and solutions:

Part a-1

Population mean = 34

(Sample mean is the best estimate for population mean.)

Part a-2

Estimate value = 34

(Sample mean is the best estimate for population mean.)

Part b-1

We need to use the t distribution because standard deviation of the population is not given from where we take a random sample.

Part b-2

We assume that the sample is come from a normally distributed population.

(Already given in the problem information)

Part c

We are given

Xbar = 34

S = 12

n = 27

df = n – 1 = 26

Confidence level = c = 98% = 0.98

= 1 – C = 1 – 0.98 = 0.02

/2 = 0.02/2 = 0.01

So, we have to find t0.01, 26 by using t-table or excel.

Value of t = 2.479

Part d

Confidence interval = Xbar -/+ t*S/sqrt(n)

Confidence interval = 34 -/+ 2.479*12/sqrt(27)

Confidence interval = 34 -/+ 2.479* 2.309401077

Confidence interval = 34 -/+ 5.724

Lower limit = 34 - 5.724 = 28.276

Upper limit = 34 + 5.724 =39.724

Confidence interval for the population mean is 28.276 and 39.724.

Part e

Yes

It would be reasonable to conclude that the population mean is 36 kg, because this value is lies within the given confidence interval.

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