Question

A random sample of 100 observations produced a sample mean of 32. Find the critical and observed values of z for the following test of hypothesis using α = 0.025 . The population standard deviation is known to be 5 and the population distribution is normal. H 0 : μ = 28 versus H 1 : μ ≠ 28 .

Answer 1

Given that the random sample of n = 100 observations produced a sample mean of = 32, the population standard deviation is known to be = 5, and the population distribution is normal.

Given the Hypotheses are:

Ho : μ = 28

H1: μ ≠ 28

Based on the hypothesis it will be a two-tailed test and since the population standard deviation is known hence Z-distribution is applicable.

Test Statistic:

The calculated test Statistic will be:

Critical value:

The critical value for rejection fo the null hypothesis is calculated using excel formula for normal distribution which is -NORM.S.INV(1-/2) hence the formula used is =NORM.S.INV(1-0.025/2), thus the Z critical is computed as Zc = +/- 2.24

P-value:

The P-value is computed using excel formula for normal distribution or by Z table but since the Z score is very high so, P-value will be =0.

Conclusion:

Since P-value is less than 0.025 hence we reject the Null hypothesis.

The Z table is attached below: