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. 157 164 145 147 163 188 194 176 168 153 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? OA. No, the population is not normal. O B. No, there are outliers. ° C. No, neither condition is met. 0 D. Yes, both conditions are met. 80 250 130 230 Days Days (b) Construct a 95% confidence interval for the mean length of the growing season in the region. 0b (Use ascending order. Round to two decimal places as needed.) (c) What can be done to decrease the margin of error, assuming the researcher does not have access to more data? O A. The researcher could increase the level of confidence. OB. The researcher could decrease the level of confidence. ° C. The researcher could increase the sample mean. D. The researcher could decrease the sample standard deviation.

Explanation / Answer

a) option d Yes, both conditions are met

b)

(X - )2 = 2434.50

95% t ststic value 0.05 when df = 9 from standard ttable is 1.833

x^+- t critical value *s/sqrtn

165.50+-1.833*16.45/sqrt10

= 165.50+-9.5351

=[155.96,175.03]

c) The researcher could increase the level of confidence

option a

Mean of set () = 1655 = 165.50 10

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