Question

After the ISO9000 procedure is introduced by the Ministry of Education, the Utopia Island Teachers’ Union claims that school teachers have spent more than 2 hours on paper work every week, and as the result, the teaching quality has been affected. A random check with 50 teachers from different schools in the island has shown that teachers spent an average 2.5 hours of paperwork on weekly basis. Test whether the claim by Utopia Island Teachers’ Union is valid.

with standard deviation 1.5 hrs

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: u = 2
Alternative hypothesis: u > 2

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.2121
DF = n - 1

D.F = 49
t = (x - u) / SE

t = 2.357

where s is the standard deviation of the sample, x is the sample mean, u is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of 2.357.

P-value = P(t > 2.357)

Use the t-value calculator for finding p-values.

P-value = 0.0092

Interpret results. Since the P-value (0.0092) is less than the significance level (0.05), we have to reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that teachers spent an average 2.5 hours of paperwork on weekly basis.