Question

I would like aid with finding the significant level, test statistic, p-value using two sample means. thank you.

Answer 1

There are 2 methods for 2-sample means

1)z-test for 2 mean with known Population Standard Deviations

2) t-test for two means- Unknown Population Standard Deviations

in 2-sample t-test

there are variations

i) equal variance

ii) unequal variance

1)

z-test for 2 mean with known Population Standard Deviations

TS =

significance level is normally 0.05, but you can fix it other values like 0.01 and 0.10 also depending on maximum type i error you want to make

Type I error occurs when we reject a true null hypothesis,

The p-value is the probability of obtaining sample results as extreme or more extreme than the sample results obtained, under the assumption that the null hypothesis is true

p-value depend on whether the test is 2-tailed, left-tailed or right-tailed

2-tailed : , p-value = 2 P(Z > |TS|)

left-tailed , p-value = P(Z < TS)

right-tailed , p-value = P(Z > TS)

2)

Normally, the way of knowing whether the population variances must be assumed to be equal or unequal is by using an F-test for equality of variances.

With the above t-statistic, we can compute the corresponding p-value, which allows us to assess whether or not there is a statistically significant difference between two means.