Question

The Mayo clinic recommends that people exercise 30 minutes a day. We will assume that exercise activity levels are normally distributed (yeah, I know they are not – but humor me....). A researcher wants to test whether the amount of daily exercise by vegetarians is different from that goal. To investigate this belief, he randomly samples seven vegetarians and measures how many minutes per day they exercise. His results are: 29, 35, 36, 33, 31, 29, and 38.

(a) Which statistical test does this scenario call for?

(b) Why that statistical test? Hint: What do we know and what do we not know?

(c) State H0.

(d) State H1.

(e) Please justify your choice of H1.

(f) What are your degrees of freedom (if there are any)?

(g) What is/are the critical value(s) of your test statistic based on $\alpha$ = 0.05

(h) Which of the areas in the figure below (A, B, C, and/or D) reflect the critical region(s)? Select all that apply.

(i) Please calculate the value of each of the following. Hint: Remember, we are now doing inferential statistics.

Sample mean:

The value to which you are comparing your sample:

Standard deviation:

Standard error:

(i) What is the formula for your test statistic? Hint: It’s probably safer/easier to type it out using parentheses and “ +, -, *, or / ”, but you can write it out in English as well.

(j) What is your obtained value for your test statistic?

(k) What is your p-value?

(l) What is the statistical decision regarding H0?

(m) What is the substantive conclusion? Hint: Be certain that it does not sound like a statistical conclusion.

(n) What is the 95% confidence interval for your estimate of the number of minutes per day that vegetarians exercise?

(o) In what specific way do the results of (l) and (n) agree?

Answer 1

a) b) we The appropriate test statistic for this scenario is one sample t-lest. ust should use and sample t-test because i) it requires to compare the same mean to the population mean. population standard diviation ý unknow test the so 1) The e) Hoi M=30 d) Hi M 730 It ek a two tail test because the researches wants to test whether the am whether the amount of daily exeruse by vegetariants is different from 30 minites mean eneriese recommended the Mayo Clinic, by 8) Degree of freedom for this to the Rist is sample size (n) al = 7-156 g) critical values or t 0.056 = -2,4469 2.4469 10.09 2, 6 b) The areas of critical regions are n and Doors areas. i) Sample mean (2) at Exi= 1 x 231=33 The value to which we are comparing our samph = Mo=30 Standard deviation, a = 3.5 119 Standard enor sen) = Blon=1,3274. k)

i) Formula for test statistic, ar Mo toks SEW 7 Test statistic, tobia 33-30 = 2.2 601 1.3274 k) P-valu = 28(*> 2.2601) = 0.0645 e) The privalue 0.0845 is greater than the d=0,05. Hence, fail to reject Ho. m) conclusion. There is sufficient evidence to conclude that the of daily exercise Quercise by vegetarians is not defti different from that goal.. estimate of the number vegetasians amount n the 95%. es minutes per for our day that enruse. nttoos, SE(W) = 33+ 2.4469 x 1.3274 6 G. 331 3.25 = (29,75, 36,25) o) The valu M=30 includes in the 95% of (29.95, 36.25). Hence, the condesio porm (n) contrast from the (1). S²