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: n > 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 see whether 20 is in the interval. If so, fail to reject the null hypothesis. (c) Construct a lower one-sided confidence bound and sec whether 20 is equal to or exceeds the bound. If so, fail to reject the null hypothesis. (d) 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. (e) Construct an upper one-sided confidence bound and sec whether 23.2 is equal to or exceeds the bound. If so fail to reject the null hypothesis.

Explanation / Answer

confidence interval gives us lower bound and upper bound. value of estimator is lies between this. here alternative hypothesis is greater than 20, if lower sided bound gives 20 or greater than 20, then alternative hypothesis selected

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