A paint manufacturer’s latex paint requires 130 minutes, on average, to dry. A n

Question

A paint manufacturer’s latex paint requires 130 minutes, on average, to dry. A new additive is being tested to determine if it reduces the mean drying time of this paint. The drying times, in minutes, for a random sample of forty-five randomly selected cans of this manufacturer’s paint (with additive) are shown in the following table displays the data in minutes. Does this sample provide evidence that the additive reduces the paint’s drying time? Address parts (a) through (g). 123 109 115 121 130 104 134 122 132 127 106 120 116 136 123 118 112 127 131 128 136 110 133 125 117 131 119 122 133 119 135 109 116 105 118 113 126 117 125 111 127 131 114 110 122 (a) What are the null and alternative hypotheses? Use the appropriate symbols to write each. B) What is the sampling distribution (the Binomial Distribution, Normal Distribution, T Distribution)? Why? c) Check the assumptions necessary for inference. That is, check the requisite conditions for performing this hypothesis test. Justify each for this specific problem. d) Compute the P-value; report your answer with at least five digits after the decimal point. e) Either use the appropriate symbols and values to communicate the specific conditional probability that the P-value represents in this particular problem or write a sentence, or two, describing the specific event – in the context of this problem – which has probability equal to the P-value of occurring. f) If you decide to perform this hypothesis test at the 1% level of significance, what do you conclude? Please write your conclusion in plain English about whether-or-not the additive reduces the average drying time of this manufacture’s latex paint. g) If the paint additive doesn’t actually reduce the drying time of this manufacturer’s latex paint, have you made an error? Explain. [If you have made an error, tell which kind of error (Type I or Type II) you made.]

Explanation / Answer

A) HERE THE H0: U= 130

Ha: U<130

B) THE DISTRIBUTION WILL BE NORMAL DISTRIBUTION AS THIS IS THE CONDITION FOR HYPOTHESIS TESTING.

C) THE CONDITION TO BE MET FOR THE HYPOTHESIS TESTING =

1) SAMPLE SIZE SHOULD BE GREATER THEN 40, WHICH IS TRUE IN THIS CASE.

2) THE DISTRIBUTION WILL BE OF NORMAL DISTRIBUTION, TRUE

D) NOW FOR THE P VALUE

WE WILL CALCULATE THE STANDARD DEVIATION OF THE DATA

THE T TEST = (X-MEAN)/(STANDARD DEV/SQRT(N)) = (121.28 - 130)/(9/SQRT(45)) = -6.50

THE DEGREE OF FREEDOM = 45-1 = 44

ALPHA = 0.05

P VALUE TO BE TAKEN FROM T TABLE

= P VALUE = 0.000001

WE WILL ACCEPT THE NULL HYPOTHESIS.

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