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?

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

(e) Compute the P-value; report your answer with at least four digits after the decimal point. Write a sentence, or two, describing the process you used to determine the P-value. If, for example, you use a TI-84+ calculator or an iOS app or an Android app or Excel or StatCrunch, etc., state this, give the name of the specific function within that technology that you use, and describe the information you had to enter in order to execute the function. If, instead, you use an online app, provide the URL and describe the information you had to enter in order to execute the function. [1.5 pts]

(f) Use the appropriate symbols and values to communicate the specific conditional probability that the P-value represents in this specific problem and write a sentence, or two, describing the specific event in the context of this specific problem which has probability equal to the P-value of occurring. [1 pt]

(g) If this hypothesis test is performed 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. [1.5 pts] (h) If the paint additive does not, in fact, reduce the drying time of this manufacturer’s latex paint, have you made either a Type I or Type II error in part

(h)? If you have made an error, tell which kind of error (Type I or Type II) you made and explain why; if no error has been made, explain why

Answer 1

e) To compute the p-value, we need to calculate the z score.

Following is the formula:

The target value and standard deviation can be calculated using excel:

Step 1: Put the data into the spreadsheet

Step 2: Mean can be determined by using the following formula (=average)

Step 3: The standard deviation can be determined by using (=stdev.s)

Putting the values in the z score formula, we get:

By referring to the standard normal table, the p-value at z=-0.96773 is 0.16672

f) The probability that the paint's drying time will be less than 130 minutes is 0.16672

g) At 1% level of confidence

Since the p-value is more than the level of significance, the null hypothesis will be accepted.

Which means that the mean drying time is 130 minutes

h) Type 2 error can be made here, that the null hypothesis is accepted even if nulll hypothsis is actually false.