1. You work for a consumer advocate agency and want to findthe mean repair cost
ID: 2955326 • Letter: 1
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1. You work for a consumer advocate agency and want to findthe mean repair cost of a washing machine. As part of your study,you randomly select 35 repair costs and find the mean to be$124.00. The sample standard deviation is $17.10. Complete parts(s) and (b). a. Construct a 95% confidence interval for the population meanrepair cost. The 95% confidence interval is ___-___ (Round to two decimalplaces as needed.) b. Change the sample size to n= 70. Construct a 95% confidenceinterval for the population mean repair cost. The 95% confidence interval is ___-____ (Round to two decimalplaces as needed.) Which confidence interval is wider? The n= 70 confidenceinterval is wider because a larger sample is taken, giving moreinformation about the population. Or The n= 35 confidence intervalis wider because a smaller sample is taken, giving less informationabout the population. Or the two intervals are the same sizedbecause the confidence interval is based on the level of confidenceand sample standard deviation. 1. You work for a consumer advocate agency and want to findthe mean repair cost of a washing machine. As part of your study,you randomly select 35 repair costs and find the mean to be$124.00. The sample standard deviation is $17.10. Complete parts(s) and (b). a. Construct a 95% confidence interval for the population meanrepair cost. The 95% confidence interval is ___-___ (Round to two decimalplaces as needed.) b. Change the sample size to n= 70. Construct a 95% confidenceinterval for the population mean repair cost. The 95% confidence interval is ___-____ (Round to two decimalplaces as needed.) Which confidence interval is wider? The n= 70 confidenceinterval is wider because a larger sample is taken, giving moreinformation about the population. Or The n= 35 confidence intervalis wider because a smaller sample is taken, giving less informationabout the population. Or the two intervals are the same sizedbecause the confidence interval is based on the level of confidenceand sample standard deviation.Explanation / Answer
sample mean, x=124,standard deviation, s=17.1,
sample size, n =35
standard error, e = s/n = 17.1/35 = 2.89
(a) At =0.05, for a two tail distribution, z=1.96 (from z table)
The 95% confidence interval for the population mean repaircost.
= x ± (z*e)
= 124 ± (1.96 * 2.89)
= (118.34, 129.66)
(b) if sample size to n= 70
standard error, e = s/n = 17.1/70 = 2.04
The 95% confidence interval for the population mean repair cost
= x ± (z*e)
= 124 ± (1.96 * 2.04)
= (120, 128)
The n= 35 confidence interval is wider because a smaller samplesize has been taken
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