An agricultural researcher is interested in estimating the m

An agricultural researcher is interested in estimating the mean length of the growing season in a region. Treating the last 10 years as a simple random sample, he obtains the following data, which represents the number of days of the growing season. 151, 161, 150, 146, 164, 185, 191, 176, 170, 147

A) Because the sample size is small, we must verify that the data come from a population that is normally distributed and that the sample size does not contain any outliers. Are the conditions for constructing a confidence interval about the mean satisfied?

a) No, there are outliers.

b) No, neither condition is met.

c) Yes, both conditions are met.

d) No, the population is not normal.

B) Construct a 95% confidence interval for the mean length of the growing season in the region: (___,___) C) What can be done to decrease the margin of error, assuming the researcher does not have access to more data?

a) The researcher could decrease the level of confidence.

b) The researcher could increase the level of confidence.

c) The researcher could decrease the sample standard deviation.

d) The researcher could increase the sample mean.

Solution

A) Because the sample size is small, we must verify that the data come from a population that is normally distributed and that the sample size does not contain any outliers. Are the conditions for constructing a confidence interval about the mean satisfied?

c) Yes, both conditions are met. [answer]

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B) Construct a 95% confidence interval for the mean length of the growing season in the region: (___,___)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    164.1          
t(alpha/2) = critical t for the confidence interval =    2.262157163          
s = sample standard deviation =    16.11383119          
n = sample size =    10          
df = n - 1 =    9          
Thus,              
              
Lower bound =    152.5728596          
Upper bound =    175.6271404          
              
Thus, the confidence interval is              
              
(   152.5728596   ,   175.6271404   ) [ANSWER]

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C) What can be done to decrease the margin of error, assuming the researcher does not have access to more data?

a) The researcher could decrease the level of confidence. [answer]