The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the

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The mean drying time of a brand of spray paint is known to be 90 seconds. The research division of the

company that produces this paint contemplates that adding a new chemical ingredient to the paint will

accelerate the drying process. To investigate this conjecture, the paint with the chemical additive is sprayed

on 15 surfaces and the drying times are recorded. The mean and standard deviation computed from these

measurements are 86 and 4.5 seconds, respectively. Assume the measurements constitute a random sample

from a normal population. Answer the following questions.

 

a) Define µ in the context of this problem.

(b) What is the point estimate for the mean drying time of the spray paint with the new chemical ingredient?

(c) Construct a 98% confidence interval for the mean drying time of the paint with the chemical additive.

Is µ included in this interval?

(d) Do these data provide strong evidence that the mean drying time is reduced by the addition of the new

chemical? Perform the hypothesis testing (at the significance level α = .02) by answering the questions

arranged in the following.

i. Formulate the null and alternative hypotheses.

ii. State the Type I error and Type II error in the context of the problem and tell why Type I error is

more serious.

iii. State the test statistic and its distribution.

iv. Determine the critical value for α = .025 and state the decision rule.

v. Calculate the observed value of the test statistic from the data.

vi. State whether H 0 is rejected and tell why.

Readings: Section 10.3.

2. Rural and urban students are to be compared on the basis of their scores on a nationwide musical aptitude

test. Two random sample of sizes 90 and 100 are selected from rural and urban seventh grade students. The

summary statistics from the test scores are

Table

Rural

Urban

Sample Size

90

100

Mean

76.4

81.2

Standard deviation

8.2

7.6

 

Answer the following questions.

(a) Define µ 1 and µ 2 in the context of the problem.

(b) What is the point estimate for µ 1 − µ2?

(c) Construct a 97% confidence interval for µ 1 − µ 2 . Is µ included in this interval?

(d) Do these data provide strong evidence that there is a difference in population mean scores between urban

and rural students? Perform the hypothesis testing (at the significance level α = .01) by answering the

questions arranged in the following.

i. Formulate the null and alternative hypotheses.

ii. State the test statistic and its distribution.

iii. Determine the critical value for α = .01 and state the decision rule.

iv. Calculate the observed value of the test statistic from the data.

v. State whether H 0 is rejected and tell why.

 

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