The following data from the Census bureau represents the total annual payroll fr

Question

The following data from the Census bureau represents the total annual payroll from some California counties in 2015 The data has been transformed to make it look more normal. We want to test whether there was a statistically significant increase in payrolls from 2015 to 2016. Assuming that the variance in both samples is 0.5, calculate a test statistic for testing H_0: mu_2015 = mu_2016 vs. H_1: mu_2015 notequalto mu_2016. Find a P value using the appropriate normal distribution. If instead we assume that the variances in both samples are the same but that we don't know what they are, calculate the pooled estimate of the sample standard deviation. Calculate the appropriate t statistics for this test when we estimate the s_pool. What do you conclude? (Use alpha = 0.05 level)

Explanation / Answer

MS Excel formula:

2015 2016 5.8949 5.9428 5.9822 6.006 6.4269 6.451 6.7192 6.753 6.769 6.8098 7.0776 7.0913 7.2107 7.2559 7.2501 7.282 7.8076 7.8352 8.2101 8.2427 Mean= 6.93483 6.96697 SD= 0.738231 0.737005 H0: There is no diff in census Ha: there is significant diff This is a 2 sided t-test with Normality assumption of distribution (a) Assuming var_A= var_B =.5 pooled variance=.5 pooled SD= 0.707107 SE (std error)= 0.316229 t-stat= =mean difference/SE (Std error) 0.101635 P-value= 0.920166 (b) pooled SD S1= 0.738231 S2= 0.737005 Pooled var= 0.544081 pooled SD= 0.737631 (C ) Using above pooled SD, we compute SE (std error)= 0.329878 t-stat= =mean difference/SE (Std error) 0.09743 (d) P-value based on above t-stat = 0.923798 P-value> 0.05; cant reject H0; so conclusion is there is no significant diff in both census

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