Statistics 13 Solution for Homework #5

Since the interval falls completely in the interval (0,l ), the normal distribution will beadequate.To determine if the coat index differs from .5, we test:p-po .479-.5 1The test statistic is z = - . - -.36The rejection region requires ~$2 = .05/2 = .025 in each tail of the z distribution. From TableIV, Appendix A, 2025 = I .96. The rejection region is z < -1.96 6r z > 1.96.Since the observed value of the test statistic does rlot fall in the rejection region (z = -.36 P:-1.96), Ho is not rejected. There is insufficient evidence to indicate that the coat index differsfrom .5 at a= .05.For the Bottom of the Core:First, check to see if the normal approxi~natioll is adequate:Since the interval falls co~npletely in the interval (0,l ), the normal distribution will beadequate.To determine if the coat index is less than .5, we test:The test statistic is z =The rejection region requires a= .05 in lhe lower tail of'the z distribution. From Table IV.Appendix A, zoj - 1.645. The rejectiorl region is z < -1.645.Since the observed value of the test statictic fklls in the re-jection region (z = -2.56 < -1.645),Ho is rejected. There is sufficient evidence to indicate that the coat index is less than .5 ata= .05.