Question

Jenny wants to compare the amount of weight people lose at her gym using two popular, non-overlapping weight-loss programs, Shred It and Burn It. She randomly samples people who use each program and tracks their weight loss. Here is a summary of the results:

	Shred it	Burn it
mean	10kg	7kg
standard deviation	3.5kg	5.7kg
number of people	35	35

Jenny wants to use these results to carry out a two-sample t test to determine if the mean weight losses are significantly different for the two programs.

Answer 1

Ho: Mean_{shared it} = Mean_{Burn it}

Ha_: Mean_{shared it} =/= Mean_{Burn it}

t = (Xbar_{shared it} - Xbar_{Burn it})/(sqrt(sd_{shared it}^2/n1+sd_{Burn it}^2/n2))

=(10-7)/(sqrt(3.5^2/35+5.7^2/35))

=2.653428

Checking for the t value at 95% conf interval for 2.5% area each towards upper and lower tail with df=n-1=34

We get tck=-2.032245 and tck=+2.032245

Since t value is not in the range of -2.032245 and 2.032245 and hence we have tp reject Ho

Hence we can say that the mean wt loss are significantly different

Hope the above answer has helped you in understanding the problem. Please upvote the ans if it has really helped you. Good Luck!!