Question

The sample mean and standard deviation from a random sample of 32 observations from a normal population were computed as x¯=26 and s=9. Test whether there is enough evidence to infer at the 10% significance level that the population mean is greater than 23. Find the critical region. (e.g. t > 1 for a one-tailed test, or t < -1 or t > 1 for a two-tailed test.)

Answer 1

There is enough evidence to infer at the 10% significance level that the population mean is greater than 23

Explanation:

Given that the sample mean is 26 and sample std dev = 9

i.e

`\bar x = 26\\s=9\\n = 32\\se = (9)/(√(32) ) =1.591`

`H_0: \bar x = 23\\H_a: \bar x >23`

(Right tailed test at 10% significance level)

Mean diff = 3

Test statistic t =
`(3)/(1.591) \\=1.886`

Critical region is t>1.310

df 31

p value = 0.034

Since p <0.10 reject null hypothesis

There is enough evidence to infer at the 10% significance level that the population mean is greater than 23

Critical region is in the enclosed file