Paint used to paint lines on roads must reflect enough light to be clearly visib

Question

Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let mu denote the true average reflectometer reading for a new type of paint under consideration, A test of H_0:mu = 20 versus H_A: mu > 20, from a sample of 15 observations, gave t = 23.2. Using a confidence interval to test the hypothesis, (a) Construct a two-sided confidence interval and see whether 23.2 is in the interval. If so, reject the null hypothesis. (b) Construct a two-sided confidence interval and sec whether 20 is in the interval. If so, fail to reject the null hypothesis. Construct a lower one-sided confidence bound and see whether 20 is equal to or exceeds the bound. If so, fail to reject the null hypothesis. Construct an upper one-sided confidence bound and see whether 20 is equal to or exceeds the bound. If so, fail to reject the null hypothesis. (c) Construct an upper one-sided confidence bound and see whether 23.2 is equal to or exceeds the bound. If so fail to reject the null hypothesis.

Explanation / Answer

Here t = 23.2

Here the answer c is correct. As we have to create a one sided confidence interval around paint reflection and if vaue of 20 comes under that bound than it is ok or otherwise we will reject the null hypothesis.

HEre t = 23.2

so confidence interval = 23.2 - t/2 (s/sqrt(n))

Here first two options are wrong because it created two -tailed confidence interval and question is a directional one.

Here last two options are wrong because the one bound confidence interval is on sample mean not on the hypothesized mean. so for that we cannot use upper one sided confidence bound.

So, options C is correct.

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