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2. The drying time of a type of paint under specified test conditions is known to be normally distributed with mean 75 minutes. Chemists have proposed a new additive designed to decrease average drying time. Based on a random of sample of n = 50 observations, it was found that sample mean = 72.3 with an SD of 10 minutes. Let u be the population average drying time with a new additive. (a) Is the new additive effective? Formulate the null hypothesis and answer the question at the significance level a = 5%? (b) What is the power of the test at μ = 70? What does it mean? (c) What is the sample size needed in order to have a type II error of 1% at μ = 70? (d) Based on the data above, construct a 95% confidence interval for u.

2. The drying time of a type of paint under specified test conditions is known to be normally distributed with mean 75 minutes. Chemists have proposed a new additive designed to decrease average drying time. Based on a random of sample of n = 50 observations, it was found that sample mean = 72.3 with an SD of 10 minutes. Let u be the population average drying time with a new additive. (a) Is the new additive effective? Formulate the null hypothesis and answer the question at the significance level a = 5%? (b) What is the power of the test at μ = 70? What does it mean? (c) What is the sample size needed in order to have a type II error of 1% at μ = 70? (d) Based on the data above, construct a 95% confidence interval for u.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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2. The drying time of a type of paint under specified test conditions is known to be normally distributed with mean 75 minutes. Chemists have proposed a new additive designed to decrease average drying time. Based on a random of sample of n = 50 observations, it was found that sample mean = 72.3 with an SD of 10 minutes. Let u be the population average drying time with a new additive. (a) Is the new additive effective? Formulate the null hypothesis and answer the question at the significance level a = 5%? (b) What is the power of the test at μ = 70? What does it mean? (c) What is the sample size needed in order to have a type II error of 1% at μ = 70? (d) Based on the data above, construct a 95% confidence interval for u.
Transcribed Image Text:2. The drying time of a type of paint under specified test conditions is known to be normally distributed with mean 75 minutes. Chemists have proposed a new additive designed to decrease average drying time. Based on a random of sample of n = 50 observations, it was found that sample mean = 72.3 with an SD of 10 minutes. Let u be the population average drying time with a new additive. (a) Is the new additive effective? Formulate the null hypothesis and answer the question at the significance level a = 5%? (b) What is the power of the test at μ = 70? What does it mean? (c) What is the sample size needed in order to have a type II error of 1% at μ = 70? (d) Based on the data above, construct a 95% confidence interval for u.
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