Question

1) Compute the Population Mean, Variance and standard Deviation of the 20 men in seconds the subjects stayed balanced. 2) Identify a random sample of 10 men and find the sample mean (avaerage balance time in seconds) 3) Find he Median number of days per week exercised. 4) Find the Mode of the favorite exercise. 5) Construct a complete hypothesis test and determine if the two groups (population mean vs sample mean) have significantly different balance using Alpha Level -> -0.05. The Hypothesis Test should include: 1. Null and Alternative Hypothesis 2. Standard Error of the Mean 3. Standard Score 4. Alpha Level-Critical 2 (two-tail test) 5. Conclusion: a. fail to reject H, or b.reject H, 6. Conclusion with reference to original hypothesis statement if if the two groups (population mean vs sample mean) have significantly different balance times"

Answer 1

Sample mean = xbar = 6.9

Population mean = 6.75

Sample standard deviation = s = 1.911951

standard error = s/sqrt(n) = 0.604612

H₀ : There is no significance difference between balance times of population mean and Sample mean

H₁ : There is significance difference between balance times of population mean and Sample mean

sample size is n= 10 < 30 , so we use t - test

Test Statistic:

t = (xbar - μ ) / (s / √n )

t = (6.9 - 6.75 ) / (1.911951 / √10)

t = 0.2481

critical value at 5 % level of significance

t_0.05,9 = 2.2622

p - value = 0.8096

Here, p - value > α (0.05 )

hence, we fail to reject H₀

Therefore,

There is no significance difference between balance times of population mean and Sample mean