Question

Need help answering 9.86 Early-Onset Dimentia

Answer 1

Test: μ < 55 with normal dist" Hypothesis test Ha : μ < 55 This is lower tailed test (Null Hypothesis, Ho : μ-55 is also correct) (Alternative Hypothesis, also called H1) 52.5 σ 6.8 Significance Level, a 0.01 --μ 52.5-55 Test statistic z ะ-1.68477 -1.68 Test Statistic, z1.68 P-value Approach P-value is in direction of Alternative hypothesis Since Ha : μ < 55, P-value-P(Z <-1.68) P-value is Area to the left of test statistic-1.68 P-value0.0465 test statistic-1.68 P-value P(Z<-1.68) 0.0465(from z-table)

P-value 0.0465 Rejection Rule: Reject Ho if p-value < a Using excel function normdist(52.5 - 55)/(6.8/sqrt(21))),0,1, TRUE) or TI's function normalcdf1E-99, ( (52.5 - 55)/( 6.8/sqrt(21))) answer is: 0.0460164316 ecision: Silace 0,0652001, we fail to reject the mull by potlhosis Rejection Region Approach (Traditional Method) The Critical Value -Zerita0.01 (-1)*2.33 (closest value Fromz table) Critical Value-2.33 Rejection Rule: Reject Ho if z*< -2.33 (because this is lower tailed test) Rejection region has been shaded a-0.01 2-2.33 Decision: Since 1.68 -2.33, we fail to reject the nu hypothesis. Hence at 1% significance level, there is insufficient evidence to conclude that μ is less than 55