A random sample of 47 soil specimens was obtained, and the amount of organic mat

Question

A random sample of 47 soil specimens was obtained, and the amount of organic matter (%) in the soil was determined for each specimen. The sample mean is 2.481% and the sample standard deviation is 1.616%. a Find a 95% confidence interval for the true average percentage of organic matter in the soil. b Based on your confidence interval, is it plausible that the true mean percentage of organic matter in the soil is 3.5%? Explain your answer. c Conduct a hypothesis test at the alpha = 0.05 level to determine if the true mean percentage of organic matter in the soil differs from 3.5%. d Does your conclusion in part c match your answer in part b? Should it?

Explanation / Answer

a) for std error of mean =std deviation/(n)1/2 =0.2357

for 95% CI and 46 degree of freedom t=2.0129

hence confidence interval =sample mean -/+ t*std error =2.0065 ; 2.9555

b no as this is not included in our confidence interval

c) for test stat t=(X-mean)/std error =(3.5-2.481)/0.2357=4.3233

as above test stat is greater then critical value we reject null hypothesis that true mean % is 3.5%.

d)concludsion in both parts are same

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