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damaskus [11]
2 years ago
12

A test is made of H subscript 0 colon space mu space equals space 43 space space v e r s u s space space H subscript 1 colon spa

ce mu space greater than space 43. A sample of size n equals 76 is drawn, and the sample mean is 47. The population standard deviation is 25. Compute the value of the test statistic and determine if the H subscript 0 is rejected at the alpha equals 0.05 level.
Mathematics
1 answer:
sweet [91]2 years ago
4 0

Answer:

The calculated value Z = 1.39 <1.96 at 0.05 level of significance

The null hypothesis is accepted

Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the mean of the Population = 43

Given that the mean of the sample = 47

Given that the standard deviation of the Population = 25

Given that the sample size 'n' = 76

<u><em>Step(ii):-</em></u>

<u><em>Null hypothesis:H₀: μ = 43</em></u>

<u><em>Alternative Hypothesis: H₁: μ ≠ 43</em></u>

Test statistic

           Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }

          Z = \frac{47-43 }{\frac{25}{\sqrt{76} } }

          Z = 1.39

Level of significance = 0.05

The critical value = 1.96

<u><em>Final answer:-</em></u>

<em>The calculated value Z = 1.39 <1.96 at 0.05 level of significance</em>

<em>The null hypothesis is accepted </em>

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