In: Statistics and Probability
A random sample of 23 chemists from Washington state shows an
average salary of $46066 with a standard deviation of $772. A
random sample of 21 chemists from Florida state shows an average
salary of $40860 with a standard deviation of $772. A chemist that
has worked in both states believes that chemists in Washington make
a different amount than chemists in Florida. At αα=0.05 is this
chemist correct? Let Washington be sample 1 and Florida be sample
2.
The correct hypotheses are:
Since the level of significance is 0.05 the critical value is
2.019 and -2.019
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)
The decision can be made to:
The final conclusion is that:
Given that,
For Washington State : n1 = 23, x1-bar = $46066 and s1 = $772
For Florida State : n2 = 21, x2-bar = $40860 and s2 = $772
The null and alternative hypotheses are,
H0 : μ1 = μ2
HA : μ1 ≠ μ2 (claim)
Test statistic is,
=> The test statistic is 22.343
The p-value is 0.000
Since, p-value is less than 0.05 level of significance, we Reject H0.
The final conclusion is that : There is enough evidence to support the claim that chemists in Washington make a different amount than chemists in Florida.