A random sample of 22 chemists from Washington state shows an average salary of $46761 with a standard deviation of $891. A random sample of 17 chemists from Florida state shows an average salary of $49312 with a standard deviation of $616. A chemist that has worked in both states believes that chemists in Washington make more 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: H0:μ1≤μ2H0:μ1≤μ2 HA:μ1>μ2HA:μ1>μ2(claim) H0:μ1≥μ2H0:μ1≥μ2 HA:μ1<μ2HA:μ1<μ2(claim) H0:μ1=μ2H0:μ1=μ2 HA:μ1≠μ2HA:μ1≠μ2(claim) Since the level of significance is 0.05 the critical value is 1.688 The test statistic is: (round to 3 places) The p-value is: (round to 3 places) The decision can be made to: reject H0H0 do not reject H0H0 The final conclusion is that: There is enough evidence to reject the claim that chemists in Washington make more than chemists in Florida. There is not enough evidence to reject the claim that chemists in Washington make more than chemists in Florida. There is enough evidence to support the claim that chemists in Washington make more than chemists in Florida. There is not enough evidence to support the claim that chemists in Washington make more than chemists in Florida.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A random sample of 22 chemists from Washington state shows an average salary of $46761 with a standard deviation of $891. A random sample of 17 chemists from Florida state shows an average salary of $49312 with a standard deviation of $616. A chemist that has worked in both states believes that chemists in Washington make more 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:

H0:μ1≤μ2H0:μ1≤μ2
HA:μ1>μ2HA:μ1>μ2(claim)
H0:μ1≥μ2H0:μ1≥μ2
HA:μ1<μ2HA:μ1<μ2(claim)
H0:μ1=μ2H0:μ1=μ2
HA:μ1≠μ2HA:μ1≠μ2(claim)

Since the level of significance is 0.05 the critical value is 1.688

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

reject H0H0
do not reject H0H0

The final conclusion is that:

There is enough evidence to reject the claim that chemists in Washington make more than chemists in Florida.
There is not enough evidence to reject the claim that chemists in Washington make more than chemists in Florida.
There is enough evidence to support the claim that chemists in Washington make more than chemists in Florida.
There is not enough evidence to support the claim that chemists in Washington make more than chemists in Florida.

Expert Solution

Step 1

Given Information :

The provided sample means are shown below:

${\bar{X}}_{1}$

${\bar{X}}_{2}$

Also, the provided sample standard deviations are:

$s_{1} = 89 1 ,$ $s_{2} = 616$

and the sample sizes are $n_{1} = 22$ and $n_2 = 17$ .

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