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gayaneshka [121]
3 years ago
7

g A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam. We ar

e interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%. The test statistic is
Mathematics
1 answer:
BaLLatris [955]3 years ago
4 0

Answer:

The test statistic is z = 1.25

Step-by-step explanation:

We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%.

At the null hypothesis, we test if the proportion is 80%, that is:

H_0: p = 0.8

At the alternate hypothesis, we test if the proportion is more than 80%, that is:

H_a: p > 0.8

The test statistic is:

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

In which X is the sample mean, \mu is the value tested at the null hypothesis, \sigma is the standard deviation and n is the size of the sample.

80% is tested at the null hypothesis:

This means that \mu = 0.8, \sigma = \sqrt{0.2*0.8} = 0.4

A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam.

This means that n = 100, X = \frac{85}{100} = 0.85

The test statistic is

z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{0.85 - 0.8}{\frac{0.4}{\sqrt{10}}}

z = 1.25

The test statistic is z = 1.25

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