Question

ne increase body masur whether playing sports will decrease body mass (due to more calories burned) or 22.5 with a staue to more muscle mass). The average BMI in the general population of students is average BMI i eation of 3. The researcher interviews 60 student athletes and finds that their bod Tails: one□ μ= twoJ dt nDorn-1. Critical value. +D :0 Null Hypothesis: 一一ー In words: Alt. Hypothesis: μ# i, words. COMPUTE: Reject H Fail to Reject Ho Interpret Result: 2. A researcher in interested in whether students who are musicians have higher intelligence test scores than students in the general population. The mean for the general population is 100. The researcher selects 30 musicians from local high schools and gives them an intelligence test, with a mean of 105 with a standard deviation of 5. Test z D t Null Hypothesis: Tals: one OtwoO Critical value (a·06): +0-0 to _ df: na orn-1. μ= in words: - Alt-Hypothesis: In words: - COMPUTE Reject Ho D Fail to Reject Ho Interpret Result

Answer 1

Solution(1)
Population mean (mu) = 22.5
Population standard deviaiton(sigma) = 3
Xbar = 22
s = sigma/sqrt(n) = 3/sqrt(60) = 0.3872
N=60
We will use Z test as we know population standard deviationa and sample is greater than 30
It is two tailed test
Degree of freedom = (sample size-1) = 60-1 = 59
at alpha = 0.05 and alpha/2 = 0.025 so Zvalue should be less than -1.96 or greater than 1.96
Null hypothesis H0: mu = 22.5. In words: Body mass does not change
Alternate hypothesis H1: mu is not euqal 22.5. In words: Body mass changed.
Z = (22-22.5)/3/sqrt(60) = -0.5/3/7.7459 = -1.29
As we can see that Z stat value is is between +/- 1.96 so we are failed to reject null hypothesis.
So we can say that body mass not changed.