Question

Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college. You survey 10 of your friends and find that the average weight gain the first year was 16.2 lbs (s.d. = 2.6). How does weight gain among your friends compare to the national average? Please round to three decimal places. Compute the test statistic.

Answer 1

Answer: 1.460

Step-by-step explanation:

Given : Researchers report that on average freshman who live on campus gain 15 pounds during their first year in college.

Let $\mu$ represents the population mean .

Then, the set of hypothesis will be:-

$H_0: \mu=15$

$H_a:\mu\neq15$

We assume that this is normal distribution.

Sample size : n = 10, which is a small sample (n<30) ,s o we use t-test.

Sample mean : $\overliene{x}=16.2\ lbs$

Standard deviation : $\sigma=2.6$

The test statistic for population mean for small sample is given by :-

$t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}$

$t=\dfrac{16.2-15}{\dfrac{2.6}{\sqrt{10}}}=1.45951276623\approx1.460$

Hence , the value of test statistic = 1.460