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.

153

164

146

148

166

190

188

184

169

152

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, there are outliers.

C.No, neither condition is met.

D.No, the population is not normal.

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 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.

153

164

146

148

166

190

188

184

169

152

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. 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 condition are met No, there are outliers No, neither condition is met No, the population is not normal 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 research could decrease the level of confidence The researcher could increase the sample mean.

Explanation / Answer

By using probability plot and box plot both conditions are met

Correct option is A

Now you have to find 95% confidence interval

Formula of confidence interval is

Xbar -E < miu< xbar +E

Where E= tc * s/ sqrt(n)

By using given data you get mean(xbar) and standard deviation (s)

Using excel or any calculator you get

Xbar=165 , s= standard deviation=18.03

tc for 95% confidence leval with df=n-1=6

tc=2.447 from t table.

Plugging all values in E

You get E=16.67

Confidence interval is

( 165-16.67 , 165+16.67)

(148.33 , 181.67)

C)

If you decrease the confidence level then margin of error is also decrease.

Correct option is A

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