Question

JIS 47 women as hers. Suppose Normal dis- Do these data mothers lose cause "off- now the odor a compound hreshold for is about 25 med noses of re the DMS 15.42 Tests from confidence intervals. A confida interval for the population mean u tells us which valu of u are plausible (those inside the interval) and which values are not plausible (those outside the interval) at the chosen level of confidence. You can use this idea to carry out a test of any null hypothesis Ho: M = Mo starting with a confidence interval: reject Ho if Mo is outside the interval and fail to reject if Mo is inside the interval. The alternative hypothesis is always two-sided, H u Mo because the confidence interval extends in both directions from X. A 95% confidence interval leads to a test at the 5% significance level because the interval is wrong 5% of the time. In general, confidence level C leads to a test at signiti cance level a = 1 - C. (a) In Example 15.6 (page 380), a medical director found mean blood pressure ñ = 126.07 for an SRS of 72 executives. The standard deviation of the blood pressures of all execu tives is o = 15. Give a 90% confidence interval for the mean blood pressure u of all executives. (b) The hypothesized value un = 128 falls inside this dence interval. Carry out the z test for Ho: = 120 the two-sided alternative. Show that the test is not sigui at the 10% level. (c) The hypothesized value Ho = 129 falls outside fidence interval. Carry out the z test for Ho: M = 12 the two-sided alternative. Show that the test is sig the 10% level. ses is Nor- dence that Feater than ht sunlight not significant 129 falls outside this con for Ho: M = 129 against est is significant at

Answer 1

Rejection Region n= 72 x= 126.07 T = 15 e 16.5 Ассер арсе Region E 1.645 ( & a + Zan -1.645 (Zal is calculated using R codes a given below ) 126.07 +1.645 15 572 126-07 F 2-9080 = ) (183.162 1 R8.978) (6) Ho: Mo = 128. Hi Mo & 128 Z = X-Mo = 126.07- 128 -1.93 = -1.091762 1.767784 since falls in the . ... .. the value of z statistic Acceptance region We do not reject Ho. н ь и е. test is not significant at 10.1. level (c) Ho: Hi : Mo = 129 M. & 129 z = x - Mo 126.07- 129 = -2.93 is 1.767784 calculated value of z- statistic falls -1.657442 since in the pjection

region. . We aject to. : test is significant at 10.1 level.

qnorm(0.95) [1] 1.644854