Subject: Test of Hypothesis Solve the following problems using the appropriate t
ID: 3236498 • Letter: S
Question
Subject: Test of Hypothesis
Solve the following problems using the appropriate test of hypothesis. The mean monthly salary of a random sample of 36 faculty members of Philippine Western University is P10,000 with a standard deviation of P1,000, while the mean monthly salary of a random sample of 35 faculty members of Central Luzon University is P10, 500 with a standard deviation of P1, 200. Is there a significant difference in the mean salaries received by the teachers of the two schools? From a research survey, it was found that a random sample of 18 elementary graduates of an exclusive private school has a mean NEAT score of 90 with a standard deviation of 16, while a random sample of 24 elementary graduates of a public school showed a mean NEAT score of 85 with a standard deviaton of 12. Is there a significant difference in the NEAT performance of these two groups of elementary graduates?Explanation / Answer
Solution:-
1)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = 262.53
DF = 69
t = [ (x1 - x2) - d ] / SE
t = - 1.90
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 69 degrees of freedom is more extreme than -1.90; that is, less than -1.90 or greater than 1.90.
Thus, the P-value = 0.061
Interpret results. Since the P-value (0.061) is greater than the significance level (0.05), we have to accept the null hypothesis.
From the above test we have sufficient evidence in the favor of the claim that there is significance difference between mean salaries recieved by teachers of two schools.