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 days of the growing season. 158 162 145 155 144 172 184 188 185 171 155 Click the icon to view the table of areas under the t - distribution. (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. The normal probability plot and boxplot are shown below. Are the conditions for constructing a confidence interval about the mean satisfied? A. Yes, both conditions are met. B. No, the population is not normal. C. No, there are outliers. D. No, neither condition is met. (b) 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.) (c) What can be done to the margin of error assuming the researcher does not have access to more data? A. The researcher could increase the sample mean. B. The researcher could decrease the sample standard deviation. C. The researcher could decrease the level of confidence. D. The researcher could increase the level of confidence.

Explanation / Answer

a) Yes, both the conditions are met.

Option A is correct.

b) The statistical software output for this problem is:

One sample T confidence interval:
: Mean of variable

95% confidence interval results:

Hence,

95% confidence interval will be:

(154.83, 177.97)

c) Option C is correct.

Variable Sample Mean Std. Err. DF L. Limit U. Limit var4 166.4 5.1146847 9 154.82978 177.97022

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