Question

Consider a paint-drying situation in which dying time for a test specimen is normally distributed with σ sample of n 25 observations 75 are to be tested using a random 7. The hypotheses Ho μ-75 and Ha μ (a) How many standard deviations (of x) below the null value is x 72.3? (Round your answer to two decimal places.) 1.93 standard deviations (b) Ifx 72.3, what is the conclusion using a 0.0047 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) P-value-0268 State the conclusion in the problem context z 193 O Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75. e Do not reject the nuil hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75. O Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75 O Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75 (c) For the test e with a o.004, what is p(70)? (Round your answer to four decimal places) 70) (d) Ifthetest procedure with α-0 004 is used, what n is necessary to ensure that武70)-0.017(Round your answer up to the next whole number.) specimens e) If a level 0.01 test is used with n-100, what is the probability of a type 1 error when μ-767 Round your answer to our decimal place.)

Answer 1

c)

Hypothesized mean true mean standard deviation sample size standard error of mean for 0.004 level and left tailed test critival value Za rejection region: u+Za*ax or type Il error-probability of not rejecting B - P(Z (71.2871- Ha)/oI)) 75 70 7 25 1.4000 -2.65 71.2871 En - P(Z >0.92) 0.1788

d)

n=49

e)

type I error =0.0001