Question

1) Test the claim that the proportion of people who own cats is smaller than 80% at the 0.01 significance level.

a) The null and alternative hypothesis would be:

H0:p=0.8

H1:p≠0.8

H0:μ=0.8

H1:μ≠0.8

H0:μ≤0.8

H1:μ>0.8

H0:p≥0.8

H1:p<0.8

H0:μ≥0.8

H1:μ<0.8

H0:p≤0.8

H1:p>0.8

b) The test is:

2) Based on a sample of 500 people, 75% owned cats

a) The test statistic is: ________ (to 2 decimals)

b) The p-value is: _________ (to 2 decimals)

3) Based on this we:

Reject the null hypothesis

or

Fail to reject the null hypothesis

Answer #1

n= 500, = 0.75, P = 80% = 0.80, = 0.01

1)

a)

The null and alternative hypothesis is

**Ho:
P **** 0.8**

**H1: P
< 0.8**

b)

The test is: one sample Proportion z test

2)

a)

formula for test statistics is

**test statistics: z =
-2.80**

b)

calculate P-Value

P-Value = P(z < -2.80)

using z table we get

P(z < -2.80) = 0.0026

P-Value = 0.0026

rounding to 2 decimal

**P-Value = 0**

3)

decision rule is

Reject Ho if ( P-value ) ( )

here, ( P-value= 0 ) < ( = 0.01)

Hence, we can say,

**Reject the null
hypothesis**

Test the claim that the proportion of people who own cats is
smaller than 80% at the 0.005 significance level.
The null and alternative hypothesis would be:
H0:μ=0.8H0:μ=0.8
H1:μ≠0.8H1:μ≠0.8
H0:μ=0.8H0:μ=0.8
H1:μ<0.8H1:μ<0.8
H0:μ=0.8H0:μ=0.8
H1:μ>0.8H1:μ>0.8
H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8
H0:p=0.8H0:p=0.8
H1:p>0.8H1:p>0.8
H0:p=0.8H0:p=0.8
H1:p<0.8H1:p<0.8
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 200 people, 73% owned cats
The p-value is: (to 2 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis

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

Test the claim that the proportion of men who own cats is
smaller than the proportion of women who own cats at the .05
significance level.
The null and alternative hypothesis would be: H0:?M=?F H1:?M??F
H0:pM=pF H1:pM?F H0:pM=pF H1:pM?pF H0:pM=pF H1:pM>pF H0:?M=?F
H1:?M<?F
The test is: two-tailed left-tailed right-tailed Based on a
sample of 80 men, 45% owned cats Based on a sample of 80 women, 65%
owned cats
The test statistic is: (to 2 decimals)
The p-value is: (to...

Test the claim that the proportion of people who own cats is
significantly different than 80% at the 0.2 significance
level.
The null and alternative hypothesis would be:
H0:p=0.8H0:p=0.8
Ha:p≠0.8Ha:p≠0.8
H0:μ≤0.8H0:μ≤0.8
Ha:μ>0.8Ha:μ>0.8
H0:μ=0.8H0:μ=0.8
Ha:μ≠0.8Ha:μ≠0.8
H0:p≥0.8H0:p≥0.8
Ha:p<0.8Ha:p<0.8
H0:μ≥0.8H0:μ≥0.8
Ha:μ<0.8Ha:μ<0.8
H0:p≤0.8H0:p≤0.8
Ha:p>0.8Ha:p>0.8
The test is:
right-tailed
two-tailed
left-tailed
Based on a sample of 300 people, 82% owned cats
The p-value is: (to 2 decimals)
Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis

Test the claim that the proportion of men who own cats is
smaller than 80% at the .05 significance level. The null and
alternative hypothesis would be: H 0 : μ = 0.8 H 1 : μ < 0.8 H 0
: p = 0.8 H 1 : p ≠ 0.8 H 0 : μ = 0.8 H 1 : μ > 0.8 H 0 : p =
0.8 H 1 : p > 0.8 H 0 : μ =...

Test the claim that the proportion of people who own cats is
smaller than 10% at the 0.05 significance level.
The null and alternative hypothesis would be:
H0:p≥0.1H0:p≥0.1
H1:p<0.1H1:p<0.1
H0:p=0.1H0:p=0.1
H1:p≠0.1H1:p≠0.1
H0:μ≤0.1H0:μ≤0.1
H1:μ>0.1H1:μ>0.1
H0:p≤0.1H0:p≤0.1
H1:p>0.1H1:p>0.1
H0:μ≥0.1H0:μ≥0.1
H1:μ<0.1H1:μ<0.1
H0:μ=0.1H0:μ=0.1
H1:μ≠0.1H1:μ≠0.1
The test is:
right-tailed
left-tailed
two-tailed
Based on a sample of 100 people, 9% owned cats
The p-value is: (to 2 decimals)
Based on this we:
Reject the null hypothesis
Fail to reject the null hypothesis

Test the claim that the proportion of men who own cats is
smaller than the proportion of women who own cats at the .01
significance level.
The null and alternative hypothesis would be:
H0:μM=μF
H1:μM≠μF
H0:pM=pF
H1:pM>pF
H0:μM=μF
H1:μM<μF
H0:μM=μF
H1:μM>μF
H0:pM=pF
H1:pM<pF
H0:pM=pF
H1:pM≠pF
The test is:
left-tailed
two-tailed
right-tailed
Based on a sample of 60 men, 40% owned cats
Based on a sample of 40 women, 50% owned cats
The test statistic is: (to 2 decimals)
The p-value is: (to...

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: H 0 : p ≤ 0.7 H 1
: p > 0.7 H 0 : p = 0.7 H 1 : p ≠ 0.7 H 0 : μ = 0.7 H 1 : μ ≠
0.7 H 0 : μ ≥ 0.7 H 1 : μ < 0.7 H 0 : μ ≤...

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 people who own cats is
smaller than 80% at the 0.05 significance level. The null and
alternative hypothesis would be: H 0 : μ = 0.8 H 1 : μ ≠ 0.8 H 0 :
p ≥ 0.8 H 1 : p < 0.8 H 0 : μ ≤ 0.8 H 1 : μ > 0.8 H 0 : p =
0.8 H 1 : p ≠ 0.8 H 0 : μ ≥...

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