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Answer :
The test statistic for this hypothesis test is approximately z = 3.5355.
To calculate the test statistic for this hypothesis test, we can use the formula for the z-test for a population mean:
[tex]\[ z = \frac{{\bar{x} - \mu}}{{\frac{{\sigma}}{{\sqrt{n}}}}} \][/tex]
where:
- [tex]\( \bar{x} \)[/tex] is the sample mean (1050 in this case),
-[tex]\( \mu \)[/tex] is the population mean (1000, the national average),
-[tex]\( \sigma \)[/tex] is the population standard deviation (100 in this case), and
- [tex]\( n \)[/tex] is the sample size (50 in this case).
Substituting the given values into the formula, we get:
[tex]\[ z = \frac{{1050 - 1000}}{{\frac{{100}}{{\sqrt{50}}}}} \][/tex]
[tex]\[ z = \frac{{50}}{{\frac{{100}}{{\sqrt{50}}}}} \][/tex]
[tex]\[ z = \frac{{50}}{{10 \sqrt{2}}} \][/tex]
z ≈ [tex]\frac{{50}}{{14.1421}}[/tex]
z ≈ 3.5355
Therefore, the test statistic for this hypothesis test is approximately z = 3.5355.
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