Problems of Estimation Help with question (a), (b) & (c) The following data are

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Problems of Estimation

Help with question (a), (b) & (c)

The following data are weight (g) of 10 pieces of chocolate sampled from a large population of pieces. 45 25 34 36 43 30 50 10 36 67 Descriptive statistics of the sample (10 pieces) Sample mean = 37.6g Standard deviation = 15.269g Coefficient of Variation = 40.61% Medium = 36g Q1 = 28.75g Q3 = 46.25g (a) Estimate the range of weights for which you would expect only 5% of individual pieces in the population to be below the lower bound and the same percentage above the upper bound. (b) Should you use the normal (z value) or t distribution in calculating the range in part (c)? Explain your reasoning. (c) Calculate a 95% Confidence Interval for the population mean weight of chocolate pieces. If I asserted that the true mean was really 33.4g would you agree or disagree with my assertion? Justify your answer. SHOW YOUR WORKING FOR ALL OF THE CALCULATIONS

Explanation / Answer

for above std error =std deviation/(n)1/2 =4.828

and for 90% CI at 9 degree of freedom t=1.833

hence confidence interval =mean +/- t*std error =28.7488 ; 46.4512

b)we should use the t distribution as we do not know population std deviation as well sample size is less then 30

c) fro 95% CI, t=2.2622

hence confidence interval=26.6772 ; 48.5228

we can not disagree with you cause our confidence interval contain the value suggested by you

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