Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in minutes). These are listed here. Determine the 95% confidence interval estimate of the population mean.

Complete Question

Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn and each reported the amount of the time spent at part-time jobs (in minutes). These are listed here 180, 130, 150, 165, 90, 130, 120, 60, 200, 180, 80, 240, 210, 150, 125. Determine the 95% confidence interval estimate of the population mean.

The 95% confidence interval is  

Step-by-step explanation:

From the question we are told that

   The standard deviation is  

   The sample size is  n  = 15

     The data given is   180, 130, 150, 165, 90, 130, 120, 60, 200, 180, 80, 240, 210, 150, 125

Generally the sample mean is mathematically represented as

=>          

=>          

From the question we are told the confidence level is  95% , hence the level of significance is    

=>  

Generally from the normal distribution table the critical value  of   is  

Generally the margin of error is mathematically represented as  

=>    

=>    

Generally 95% confidence interval is mathematically represented as