Question

# Suppose a random sample of 12 male runners of college-age gave a mean weight of 151...

Suppose a random sample of 12 male runners of college-age gave a mean weight of 151 lbs with a standard deviation of 9 lbs. We would like to know whether or not the population from which this sample was selected has a lower mean weight than 160 lbs which is the mean weight of the population of college-aged males as a whole.

The value of the t-statistic for testing the hypotheses of interest is t = -3.5. What is the correct conclusion?

a. There is no significant difference between the mean weight of the runners and the mean weight of the population as a whole.

b. Runners have a significantly lower mean weight than the mean of the population as a whole.

What is the 95% confidence interval for the mean weight of the population of runners? (Show work)

According to given situation,

Null hypothesis;H0: mu= 160 lbs

Vs

Alternative hypothesis;H1:mu<160 ( left tailed)

Given, t- statistic= -3.5

So, p- value = P( t<-3.5)= 0.002485 ( using t table for alpha= 0.05 and df= (12-1=11))

Since, p- value <alpha so, we reject Therefore,We conclude that Runner have significantly lower weight than mean of population whole.

So, option b is correct.

Critical t- value for 95% confidence interval= t( alpha= 0.05) df (12-1=11) = 2.201

95% confidence for population mean is given by

x_ bar ± t( 0.05)* std. error ( x bar)

= x_bar ± t( 0.05)* s/√n

= 151 ± 2.201*(9/√12)

= 151± 5.718

= (145.282, 156.718) is required 95% confidence interval for population mean weight of runner.