Question

Income tax returns show that the mean income of self-employed persons in a particular year was £15,000, with a standard deviation of £975. A random sample of 169 returns from people in the clothing industry gave a mean income of £14,500. Did this indicate that income from self-employment in the clothing industry was significantly different?

Answer 1

Yes, There is significant difference.

Explanation:

Null Hypothesis , H0 : Mean income = 15000

Alternate Hypothesis , H1 : Mean income ≠ 15000

t = (x - u) / ( s / √n)

x = sample mean = 14500 here, u = population mean = 15000 here , s = standard deviation = 975 here , n = sample size

t = (14500 - 15000) / (975 / √169)

-500 / 75 = - 6.66

As calculated t value in absolute terms is > 1.96 , ie tabulated value at 95% significance level (two sided). So we reject the null hypothesis in favor of alternate hypothesis. Hence, we state that 'Mean Income ≠ 15000'