27. The growing season of a crop for a of 1 sample mean of 190.7 days. The popul

Question

27. The growing season of a crop for a of 1 sample mean of 190.7 days. The population standard de random sample of 10 US cities were recorded, yielding a deviation is 54.2 days a. Estimate the true mean of the b. What is the sui growing season for all US cities with a 95% confidence. table sample size to ensure that at a significance level of 5%, the max erro in the estimation in (a) is equal to 15 days? 41: 9 Repeat the above sample variance is 54.2 days problem, But, now, we do not know the true variance of the population. The

Explanation / Answer

Ans:

a)As we know population standard deviation,we can use z multiplier.

z value for 95% CI is 1.96

95% CI for true mean

=190.7+/-1.96*54.2/sqrt(10)

=190.7+/-33.6

=(157.1, 224.3)

b)Sample size required=(1.96*54.2/15)^2=50.2

sample size required=50

When true standard deviation is unknown and n<30,we use t distribution.

t value for 95% CI and df=10-1=9 is 2.262

95% CI for true mean

=190.7+/-2.262*54.2/sqrt(10)

=190.7+38.8

=(151.9,229.5)

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