Please type the answer 3. The drying time of a certain type of paint under speci
ID: 3370197 • Letter: P
Question
Please type the answer 3. The drying time of a certain type of paint under specified test conditions is known to be normally distributed with mean value 75min and a standard deviation 9 min. Chemist have proposed a new additive designed to decrease average drying time. tested using a random sample of n 25 observations a. How many standard deviations (of) below the null value is 72.3? b. If -72.3, what is the conclusion using a 01? C. What is ? for the test procedure that rejects Ho when zs-2.88? d. For the test procedure of part what is ?(70)? If the test procedure of part (e) is used, what n is necessary to ensure that ?(70) 01?Explanation / Answer
a)
(75 - 72.3)/9 = 0.3
Hence 0.3 std. dev. below the null value
b)
z = (75 - 72.3)/9 = 0.3
Fail to reject the null hypothesis
Because z-value is greater than the critical value of -2.33
c)
alpha should be 0.002 in order to reject the null hypothesis
d)
Here, n = 25 , xbar = 75 and s = 9
Critical value is -2.3263
True mean = 70
Critical value, c = xbar + (z/t)*s/sqrt(n)
c = 75 + -2.3263 * 9/sqrt(25)
c = 70.8127
Beta or type II error is the probability of fail to reject the null hypothesis
P(X > 70.8127 | mu = 70) = 0.3258
beta = 0.3258
e)
z1 (z-value at alpha = 0.01) = -2.3263
z2 (z-value at beta = 0.01) = 2.3263
mu1 (hypothesised mean) = 75, mu2 (true mean) = 70 and sigma = 9
Sample size, n = (sigma * (z1 - z2)/(mu1 - mu2))^2
n = (9 * (-2.3263-2.3263)/(75-70))^2)
n = 70.14 i.e. 70