For each of the following scenarios, determine the value of the test statistic.
ID: 3149880 • Letter: F
Question
For each of the following scenarios, determine the value of the test statistic. On the cover sheet, you should include both the symbol and the value(s). (e g z_0 = 2.33) In your supplementary work, show your calculations for the test statistic. Determine the number of samples needed in the following situation: Detect a shift from n that is plusminus 1 unit (two-sided test) sigma is known to be 1.2 units The probability of Type terror is 0.05 and the probability of Type II error Is 0 10 5) You have conducted a study to determine whether your products are meeting the customer requirements. The customer's design states that parts must have a mean length of 220 mm. You've collected 8 samples and the mean length of the samples Is 218 mm. The va'ue of a for part length is 1.1 mm Conduct a hypothesis test with a =0.05 to see if the design requirements are being met. Your work should show all 7 steps of the hypothesis testing procedure On the cover sheet. Just write your conclusion, (i. E.. There ls/ls not sufficient evidence at the a = 0.05 level of significance to conclude that mean length For the results of your hypothesis cost In part (a), what is the p-value for this test? What is the probability of making a Type I error? What would it mean In the context of this situation (i e, in terms of mean length) if you made a Type I error? II a Type I error occurs, who Is penallted-your company or your customer who receives the pans? (Examples of "penalties" could be your company discarding parts that aren't really detective or the customer receiving parts that don't meet their specifications) Briefly explain your answer. 10 If you? Want to detect a shift of mean length from 720 mm to 219 mm. what a the probability of making an error and not detecting this shift? Based on your answer to part what Is the power of this test to detect a Shift to a mean length of 219 mm? Who Is penalized if the error In part (I) occurs, your company or your customer who receives the parts? Briefly explain your answerExplanation / Answer
3.
a)
Formulating the null and alternative hypotheses,
Ho: u = 1.5
Ha: u =/ 1.5
Getting the test statistic, as
X = sample mean = 1.31
uo = hypothesized mean = 1.5
n = sample size = 18
sigma = standard deviation = sqrt(0.3) = 0.547722558
Thus, t = (X - uo) * sqrt(n) / sigma = -1.471733672 [ANSWER]
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b)
Formulating the null and alternative hypotheses,
Ho: u >= 64
Ha: u < 64
As we can see, this is a left tailed test.
Getting the test statistic, as
X = sample mean = 60.2
uo = hypothesized mean = 64
n = sample size = 9
s = standard deviation = sqrt(5) = 2.236067977
Thus, t = (X - uo) * sqrt(n) / s = -5.098234989 [ANSWER]
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c)
Formulating the null and alternative hypotheses,
Ho: sigma = 0.8
Ha: sigma =/ 0.8
As we can see, this is a two tailed test.
Getting the test statistic, as
s = sample standard deviation = sqrt(0.66) = 0.81240384
sigmao = hypothesized standard deviation = 0.8
n = sample size = 16
Thus,
chi^2 = (N - 1)(s/sigmao)^2 = 15.46875 [ANSWER]
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