Question

In: Statistics and Probability

A random sample of 23 chemists from Washington state shows an average salary of $46066 with...

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:

  • 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 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:

  • reject H0H0
  • do not reject H0H0

The final conclusion is that:

  • There is enough evidence to reject the claim that chemists in Washington make a different amount than chemists in Florida.
  • There is not enough evidence to reject the claim that chemists in Washington make a different amount than chemists in Florida.
  • There is enough evidence to support the claim that chemists in Washington make a different amount than chemists in Florida.
  • There is not enough evidence to support the claim that chemists in Washington make a different amount than chemists in Florida.

Solutions

Expert Solution

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.


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