Question

An article published in the Washington Post claims that 45
percent of all Americans have brown eyes. A random sample of n=82
college students students found 30 who had brown eyes.

Consider testing

?0:?=.45H0:p=.45

??:?≠.45Ha:p≠.45

(a) The test statistic is z =

(b) P-value =

Answer #1

**(a)**

**The test statistic is z =**
**-1.53**

**(b)**

**P-value =** **0.1260**

Solution:

Here, we have to use one sample z test for the population proportion.

The null and alternative hypotheses for this test are given as below:

H_{0}: p = 0.45 versus H_{a}: p ≠ 0.45

This is a two tailed test.

Test statistic formula for this test is given as below:

Z = (p̂ - p)/sqrt(pq/n)

Where, p̂ = Sample proportion, p is population proportion, q = 1 - p, and n is sample size

x = number of items of interest = 30

n = sample size = 82

p̂ = x/n = 30/82 = 0.365853659

p = 0.45

q = 1 - p = 0.55

Z = (p̂ - p)/sqrt(pq/n)

Z = (0.365853659 - 0.45)/sqrt(0.45*0.55/82)

Z = -1.5316

**The test statistic is z =**
**-1.53**

**P-value =** **0.1260**

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis at 5% level of significance.

There is sufficient evidence to conclude that 45 percent of all Americans have brown eyes.

An article published in the Washington Post claims that 45
percent of all Americans have brown eyes. A random sample of n = 82
college students students found 30 who had brown eyes.
Consider testing ?0:?=.45
??:?≠.45
(a) The test statistic is z =
(b) P-value =

An article in the Washington Post on March 16, 1993 stated that
nearly 45 percent of all Americans have brown eyes. A random sample
of n=82 C of I students found 30 with brown eyes.
We test
H0:p=.45
Ha:p≠.45
(a) What is the z-statistic for this test?
(b) What is the P-value of the test?

An article in the Washington Post on March 16, 1993 stated that
nearly 45 percent of all Americans have brown eyes. A random sample
of n=82 C of I students found 30 with brown eyes.
We test
H0:p=.45
Ha:p≠.45
(a) What is the
z-statistic for this test?
(b) What is the
P-value of the test?

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We test
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Ha: p≠.45
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mod 8 question 6
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