Question

According to the 2010 US Census, the average number of residents per housingunit for the n=87 counties in Minnesota was 2.10, and the standard deviationwas 0.38. Test whether the true mean number of residents per housing unitin Minnesota in 2010 is less than the national value of 2.34 at the levelα= 0.05.

Answer 1

Given data, Sample size n=87 To test. Original Claim: Mean number of residents per housing is less than 2.34 Null Hypothesis Ho: Mean number of residents per housing is 2.34 u = 2.34 Alternative Hypothesis Hj: Mean number of residents per housing is less than 2.34; u<2.34 Mean of the given sample x=2.1 Standard Deviation s=0.38 2.1-2.34 Test statistic Z=*=*== 2 0.38/87 Z=-5.8910 Critical value = -1.65 (Z critical value at 0.05 level of significance, one-tailed test) Since Z calculated value is less than critical value we reject null hypothesis i.e., Mean number of residents per housing is less than 2.34