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Community college instructors' salaries in one state are very low, so low that educators in that state regularly complain about their compensation. The national mean is [tex]$52,328, but instructors from Mississippi claim that the mean in their state is significantly lower. They survey a simple random sample of 37 colleges in the state and calculate a mean salary of $[/tex]\[tex]$49,258$[/tex] with a standard deviation of [tex]$\$[/tex]9,510$. Test the instructors' claim at the 0.10 level of significance.

Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below.

[tex]\[
\begin{array}{l}
H _0: \mu = 52,328 \\
H _a: \mu \ \textless \ 52,328
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
To address the instructors' claim regarding the salaries, we need to set up our hypotheses for the hypothesis test. We will test whether the mean salary in Mississippi is significantly lower than the national mean of \$52,328.

Step 1: State the null and alternative hypotheses.

The null hypothesis (H₀) represents the scenario where there is no significant difference in salaries, implying that the mean salary in Mississippi is equal to the national mean salary.

[tex]\[ H_0: \mu = 52,328 \][/tex]

The alternative hypothesis (H₂) represents the claim that needs to be tested: that the mean salary in Mississippi is less than the national mean salary.

[tex]\[ H_2: \mu < 52,328 \][/tex]

Thus, the hypotheses are:

[tex]\[ \begin{array}{l} H _0: \mu=52,328 \\ H _2: \mu < 52,328 \end{array} \][/tex]
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