An agricultural researcher is interested in estimating the mean length of the gr

Question

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 represent the number of days of the growing season. 159 158 151 146 166 187 191 175 170 148 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. The normal probability plot and boxplot are shown below. Are the conditions for constructing a confidence interval about the mean satisfied? Yes, both conditions are met. No, the population is not normal. No, neither condition is met. No, there are outliers. Construct a 95% confidence interval for the mean length of the growing season in the region. (Use ascending order. Round to two decimal places as needed.) What can be done to decrease the margin of error, assuming the researcher does not have access to more data? The researcher could increase the sample mean. The researcher could decrease the level of confidence. The researcher could increase the level of confidence. The researcher could decrease the sample standard deviation.

Explanation / Answer

1.If the normal probability plot is a straight line then the data set is approximately normally distributed .Here the plot is a straight line so the data is normally distributed.

2.outliers are either 3*iqr or more above the third quartile or 3*iqr or more below the third quartile here we can clearly see that there are no such observations .***iqr=ist quartile -3rd quartile

so (a) option A

the 95% confidence interval for mean is :(xbar-1.96*s/sqrt(n),xbar+1.96*s/sqrt(n))

here xbar=mean of data=165.1

s=standard deviation=15.69

confidence interval=(155.37,174.82)

(c)option B

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