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Calculate the z-test statistic for a hypothesis test in which the null hypothesis states that the population proportion, p, equals 0.14 if the following sample information is
present
n = 200
x= 31
(Round to two decimal places as needed.)
Z=

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Answer:

The z-test statistic for a hypothesis test in which the null hypothesis states that the population proportion, p, equals 0.14 if the following sample information is present (n = 200; x = 31) is z = .6114.

Step-by-step explanation:

The z-test statistic formula is:

  • [tex]\displaystyle z=\frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]

We are given x = 31 and n = 200, so we can solve for [tex]\hat{p}[/tex] : 31/200 = .155.

The population proportion, [tex]p=.14[/tex], is given in the problem.

We can substitute the known values into the z test statistic formula:

  • [tex]\displaystyle z = \frac{.155-.14}{\sqrt{\frac{.14(.86)}{200} } }[/tex]
  • [tex]\displaystyle z=\frac{.015}{\sqrt {.000602}}[/tex]
  • [tex]z=.6114[/tex]

The z-test statistic for this problem is z = .6114.

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