It is believed that nationwide, first graders spend, on average, 3.8 hours /day

Question

It is believed that nationwide, first graders spend, on average, 3.8 hours /day watching TV. Suppose = 1.1 hours. A statistician wishes to test the hypothesis at 1% level of significance, that on average, the first graders in Indiana spend more than 3.8 hours watching TV. A random sample of 30 first graders from Indiana had a mean (TV watching time) of 4.2 hours/day.

a. Calculate the rejection criteria in terms of the sample average.

b.  Write your conclusion in the context of the problem.

If anyone could help with this, I'd really appreciate it!

Explanation / Answer

Question a)

Here population standard deviation is given so it is a z-test.

At 1% level of significance the critical z value is given by 2.326; we get this value from normal table.

The null hypothesis can be rejected if the value of the test statistics:

z   2.326

Question b)

Null Hypothesis: µ 3.8

Alternative Hypothesis: µ > 3.8

z = ( x bar - µ) / ( s/ sqrt(n))

= (4.2 – 3.8)/(1.1/sqrt(30))

= 1.99

The value of the test statistics is less than the critical value (1.99 < 2.326); we fail to reject the null hypothesis.

At 1% level of significance there is not sufficient evidence to conclude that the first graders in Indiana spend more than 3.8 hours watching TV.

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