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Sagot :
Answer:
The value of z for the given details in the problem is 2.088.
Further Explanation
In doing researches, especially if it's Quantitative Researches, the usage of statistical treatment or tools is very important. Since the statistical tool helps the researcher to achieve one of the research's goals. This is where the Hypothesis Test comes in. Hypothesis Tests is a process of decision making by drawing a conclusion from the population on the basis of the sample size.
Steps In Doing Hypothesis Testing
1. Statement of the Hypotheses
Null Hypothesis
Alternative Hypothesis
2. Finding the Critical Value
3. Computing the Test Value.
4. The decision to Reject or Accept the Null Hypothesis
5. The implication of the decision in Step 4
One of the Hypothesis Tests that has been employed by the researchers is Z - Test for a Mean. This is used to draw a conclusion from the population on the basis of the sample size. This can be used when the sample size is normally distributed and the standard deviation of the population (\sigmaσ ) is known or given.
The given situation refers to Step 3 of the Hypothesis Testing. The formula that should be used in the given details in the problem is z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}z=
n
σ
x
ˉ
−μ
,
where \bar{x}
x
ˉ
is the sample mean, \begin{gathered}\mu\\\end{gathered}
μ
is the population mean, \begin{gathered}\sigma\\\end{gathered}
σ
is the population standard deviation, and nn is the sample size.
To solve for the value of zz , substitute the values of \bar{x}=78.2
x
ˉ
=78.2 , \mu=77μ=77 , \sigma=6σ=6 , and n=109n=109 into the formula, then simplify the right side using a scientific calculator.
Solution:
\begin{gathered}\begin{aligned}z&=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}\\z&=\frac{78.2-77}{\frac{6}{\sqrt{109}}}\\z&=\frac{1.2}{\frac{6}{\sqrt{109}}}\\z&=1.2\times{\frac{\sqrt{109}}{6}}\\z&=\frac{1.2\sqrt{109}}{6}\\z&=2.088\end{aligned}\end{gathered}
z
z
z
z
z
z
=
n
σ
x
ˉ
−μ
=
109
6
78.2−77
=
109
6
1.2
=1.2×
6
109
=
6
1.2
109
=2.088
This clearly shows that the value of zz is 2.0882.088 .
#LearnWithBrainly
To learn about the definition of hypothesis test, go to https://brainly.ph/question/1985930
To learn the formula for the sample size, go to https://brainly.ph/question/241222
To learn the qualities of a quantitative research, access the link https://brainly.ph/question/1576036
Step-by-step explanation:
hope it's helpful mark as brainly answer for favor please
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