Question

Use a? t-test to test the claim about the population mean mu at the given level of significance alpha using the given sample statistics. Assume the population is normally distributed. ?Claim: muequals51 comma 700?; alphaequals0.01????Sample? statistics: x overbarequals51 comma 436?, sequals1800?, nequals20

Answer 1

Here we assume the population is normally distributed.

So we can use t test statistic formula for small n also

Formula of t test statistic is given by:

Where = sample mean = 51436

= population mean under null hypothesis = 51700

s = sample standard deviation = 1800

n = sample size = 20

Plug these values in the above formula, we get

Degrees of freedom = n - 1 = 20 - 1 = 20

p-value = "=TDIST(0.6559,19,2)" = 0.5197 (This is the p-value for two tail test

Decision rule:

1) If p-value < level of significance ( ) then we reject null hypothesis.

2) If p-value > level of significance ( ) then we fail toreject null hypothesis.

Here p - value = 0.5197 > 0.01 so we fail to reject the null hypothesis.

Conclusion : At 1% level of significance there is not sufficient evidence to reject the mean is 51700.