SOLUTION: Population 1 had a standard deviation of 8 and population 2 had a standard deviation of 10. In a random sample of 30 units from Population 1, the mean was 50. In a random sample of

Algebra ->  Probability-and-statistics -> SOLUTION: Population 1 had a standard deviation of 8 and population 2 had a standard deviation of 10. In a random sample of 30 units from Population 1, the mean was 50. In a random sample of      Log On


   

Question 981083: Population 1 had a standard deviation of 8 and population 2 had a standard deviation of 10. In a random sample of 30 units from Population 1, the mean was 50. In a random sample of 40 units from Population 2, the mean was 48. Perform a test of hypothesis to investigate whether Population 1 has a greater mean compared to Population 2. Use a significance level of 0.05. Use z as test statistic.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
n1 = 30
xbar1 = 50
sigma1 = 8

n2 = 40
xbar2 = 48
sigma2 = 10

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Hypothesis:
H0: mu1 <= mu2
H1: mu1 > mu2

Right tailed test. Reject H0 if the test statistic z is larger than critical value


Standard Error:
SE = sqrt(((sigma1)^2)/(n1)+((sigma2)^2)/(n2))
SE = sqrt((8^2)/(30)+(10^2)/(40))
SE = 2.1525179

Test Statistic:
z=((xbar1-xbar2)-(mu1-mu2))/(SE)
z=((50-48)-0)/(2.1525179)
z=0.9291444
z=0.93


When alpha = 0.05, the critical value is 1.645 for a right tailed test.

The test statistic is NOT larger than the critical value. So we fail to reject the null hypothesis. The p-value (0.1764) is larger than alpha. This also tells us to fail to reject the null.

Decision: Fail to reject H0. Effectively the null hypothesis is "accepted"

Interpretation: Population 1 does not have a greater mean than population 2.