1. In the past, manufacturer has introduced a change in the production method an
ID: 2908004 • Letter: 1
Question
1. In the past, manufacturer has introduced a change in the production method and to determine whether the mean running time has increased as a re rs. The the mean running time for a certain type of flashlight battery has been 9.6 hou wants to perform a significance test eses are sult. The hypoth Ho: ? : 9.6 hours Ha: ? > 9.6 hours ults of the sampling lead to rejection of the nul hypothesis. Classify that conclusion as a Type I error, a Type ll erro r, or a correct decision, if in fact the mean running time has increased a) Type I Error b) Correct Decision c) Type Il error d) Not enough information 2. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To t this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors was selected. Suppose that the test statistic is -2.20. Can we conclude that Ho should be rejected at the (a) ? 0.10, (b) ? 0.05, and (c) ? 0.01 level of significance? est a) b) c) d) (a) no; (b) no; (c) no yes; (b) yes; (c) yes (a) yes; (b) yes; (c) no (a) no; (b) no; (c) yesExplanation / Answer
Q-1. CORRECT DECISION
As the results are rejecting null hypothesis So alternate hypothesis is true
So mean> 9.6 hours which the results are suggesting So decision is correct.
A Type I error wold occur if, in fact, ?=9.6 hours, but the results of the sampling lead to the conclusion that ?>9.6 hours.
A Type of II error would occur if, in fact, ?>9.6, but the results of the sampling fail to lead to that conclusion.
Q-2.
Our null hypothesis is that our sample proportion, p, is .9. Our alternative hypothesis is p<.9.
It is left tailed
(a) The z-critical value for a left-tailed test, for a significance level of ?=0.1 is
zc?=?1.28 here -2.20(<-1.28) lies in rejection region So reject Null hypothesis
(b) The z-critical value for a left-tailed test, for a significance level of ?=0.05 is
z_c = -1.64 here -2.20(<-1.64) lies in rejection region So reject Null hypothesis
(c) The z-critical value for a left-tailed test, for a significance level of ?=0.01 is
z_c = -2.33 here -2.20(>-2.33) not lies in rejection region So not reject Null hypothesis
Remember that for something to be considered significant (leading us to reject null hypothesis) then the calculated Z score must be farther away from the mean than the critical value. We call the area past the critical value the rejection region. If any calculated ratio lands here, we reject the null hypothesis because our value is significantly different from the population. If it were to land before the critical value, we would fail to reject the null.
ANSWER IS (C)
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