Question

A sample of 100 items, draw from a universe with mean value 4 and S.D 3, has a mean value 63.5. Is the difference in the mean significant at 0.05 level of significance?

Answer 1

Sample size n = 100

Sample mean `bar(x)` = 63.5

Sample SD S = 3

Population mean µ = 64

Population SD σ = 3

Null Hypothesis H₀: µ = 64 .....(the sample has been drawn from the population mean µ = 64 and SD σ = 3)

Alternative Hypothesis H₁: µ ≠ 64 ....(two tail)

i.e The sample has not been drawn from the population mean µ = 64 and SD σ = 3

The level of significance α = 5% = 0.05

Test statistic z = `(63.5 - 64)/(3/sqrt(100)`

= `(-0.5)/((3/10))`

= `(-0.5)/0.3`

= - 1.667

`|z| = 1.667`

∴ calculated z = 1.667

critical value at 5% level of significance is `"z"_("a"/2)` = 1.96

Inference:

At 5% level of significance `"Z" < "Z"_("a"/2)`

Since the calculated value is less than the table value the null hypothesis is accepted.