Question

DATA: According to data, 72.4% of the population in Kahului, Maui drive alone for their commute to work. You believe this is too high and will perform a study at a 5% level of significance.

A group of 30 people were sampled in Kahului, Maui where 21 people stated that they drive alone for their commute to work.

H0: p = 0.724

Ha: p < 0.724

pcap = 21/30 = 0.7

Test statistic,

z = (pcap - p)/(p*(1-p)/n))

z = (0.7 - 0.724)/(0.724 - (1-0.724)/30)

z = -0.03

p-value = 0.488

As p-value > 0.05, fail to reject H0

As this is left tailed test, critical value is to the left of standard curve critical value = -1.64

**Question: Graph the rejection region, p-value and
critical value. (Create the normal distribution curve) Explain why
we fail to reject the null hypothesis, the significance of this and
what the p value/ critical value indicate.**

Answer #1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H_{0} : p = 0.724

H_{a} : p < 0.724

= x / n = 21 / 30 = 0.7

P_{0} = 0.724

1 - P_{0} = 0.276

Test statistic = z

=
- P_{0} / [P_{0
*} (1 - P_{0} ) / n]

= 0.7 - 0.724 / [(0.724 * 0.276) / 30]

= -0.294

P(z < -0.29) = 0.3859

P-value = 0.3859

= 0.05

Critical value = -1.645

P-value >

Fail to reject the null hypothesis .

Find the standard deviation, upper and lower values, and include
graphical representations of the rejection region, p-value and the
confidence interval
According to data, 72.4% of the population in Kahului, Maui
drive alone for their commute to work. You believe this is too high
and will perform a study at a 5% level of significance. A group of
30 people were sampled in Kahului, Maui where 21 people stated that
they drive alone for their commute to work

1) Test the claim that the proportion of men who own cats is
significantly different than 70% at the 0.1 significance
level.
a) The null and alternative hypothesis would be:
H0:p=0.7
7H1:p<0.7
H0:μ=0.7
H1:μ>0.7
H0:p=0.7
H1:p>0.7
H0:μ=0.7
H1:μ≠0.7
H0:μ=0.7
H1:μ<0.7
H0:p=0.7
H1:p≠0.7
b)The test is:
2) Based on a sample of 70 people, 78% owned cats
a) The test statistic is: ______ (to 2 decimals)
b) The positive critical value is: ________ (to 2 decimals)
c) Based on this we:...

Test the claim that the proportion of men who own cats is
significantly different than 70% at the 0.2 significance
level.
The null and alternative hypothesis would be:
A) H0:μ=0.7H0:μ=0.7
H1:μ>0.7H1:μ>0.7
B) H0:μ=0.7H0:μ=0.7
H1:μ≠0.7H1:μ≠0.7
C) H0:μ=0.7H0:μ=0.7
H1:μ<0.7H1:μ<0.7
D) H0:p=0.7H0:p=0.7
H1:p>0.7H1:p>0.7
E) H0:p=0.7H0:p=0.7
H1:p<0.7H1:p<0.7
F) H0:p=0.7H0:p=0.7
H1:p≠0.7H1:p≠0.7
The test is:
A) right-tailed
B) two-tailed
C) left-tailed
Based on a sample of 35 people, 66% owned cats
The test statistic is: ____ (to 2 decimals)
The positive critical value is:____ (to 2...

Test the claim that the proportion of people who own cats is
smaller than 70% at the 0.10 significance level.
The null and alternative hypothesis would be:
H0:μ=0.7H0:μ=0.7
H1:μ≠0.7H1:μ≠0.7
H0:p≤0.7H0:p≤0.7
H1:p>0.7H1:p>0.7
H0:p≥0.7H0:p≥0.7
H1:p<0.7H1:p<0.7
H0:μ≤0.7H0:μ≤0.7
H1:μ>0.7H1:μ>0.7
H0:p=0.7H0:p=0.7
H1:p≠0.7H1:p≠0.7
H0:μ≥0.7H0:μ≥0.7
H1:μ<0.7H1:μ<0.7
The test is:
left-tailed
two-tailed
right-tailed
Based on a sample of 300 people, 65% owned cats
The test statistic is: (to 2 decimals)
The p-value is: (to 2 decimals)
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis

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Standard Normal Distribution
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