Question

In 2016, the mean household income in Dallas was $39,097. A researcher thinks that household income has risen since then, and that the mean household income in Dallas is higher than $39,097. She gathers income data from a random sample of 150 Dallas households. The sample has a mean household income of $40,352, and a standard deviation of 1,875. Based on this information, test the researcher's hypothesis at a significance level of .01. Be sure to include all 4 steps.

Answer 1

STEP 1

we have to test whether the  mean household income in Dallas is higher than $39,097 or not

it is a right tailed hypothesis

STEP 2

sample size is n = 150

degree of freedom = n-1

= 150-1

=149

using t critical value table, we get

t critical value = t(149) = 2.352 at 0.01 significance level

we will reject the null hypothesis if t calculated > 2.352

STEP 3

given that

test statistic t =

STEP 4

it is clear that the test statistic or t calculated is greater than the t critical value, i.e. 8.198> 2.352, this means we can reject the null hypothesis

therefore, we can conclude that there is sufficient evidence to support the claim that mean is higher than $39097