Question

In: Statistics and Probability

Test the claim that the proportion of men who own cats is significantly different than the...

Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.02 significance level.

The null and alternative hypothesis would be:

H0:μM=μFH0:μM=μF
H1:μM≠μFH1:μM≠μF

H0:pM=pFH0:pM=pF
H1:pM≠pFH1:pM≠pF

H0:pM=pFH0:pM=pF
H1:pM<pFH1:pM<pF

H0:μM=μFH0:μM=μF
H1:μM<μFH1:μM<μF

H0:μM=μFH0:μM=μF
H1:μM>μFH1:μM>μF

H0:pM=pFH0:pM=pF
H1:pM>pFH1:pM>pF



The test is:

right-tailed

two-tailed

left-tailed



Based on a sample of 60 men, 45% owned cats
Based on a sample of 60 women, 60% owned cats

The test statistic is:  (to 2 decimals)

The p-value is:  (to 2 decimals)

Solutions

Expert Solution

Solution :

Given that,

n1 = 60

Point estimate = sample proportion = 1 = 0.45

n2 = 60

Point estimate = sample proportion = 2 = 0.60

The value of the pooled proportion is computed as,

= (n11 + n22  ) / ( n1 + n2 )

= (27 + 36 ) / (60 + 60 )

= 0.525

1 - = 0.475

Level of significance = = 0.02

The null and alternative hypothesis is,

H0:μM=μF

H1:μM≠μF

This a two-tailed test.

Test statistics

z = (1 - 2 ) / *(1-) ( 1/n1 + 1/n2 )

= (0.45 - 0.60 ) / (0.525 * 0.475 ) (1/60 + 1/60 )

= -1.65

P-value

= 2* P(Z <z )

= 2* P(Z < -1.65)

= 2*0.0495

= 0.099

= 0.10

The p-value is p = 0.10, and since p = 0.10 > 0.02, it is concluded that the null hypothesis is fail to rejected.


Related Solutions

Test the claim that the proportion of men who own cats is significantly different than the...
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level. The null and alternative hypothesis would be: H0:pM=pFH0:pM=pF H1:pM>pFH1:pM>pF H0:pM=pFH0:pM=pF H1:pM<pFH1:pM<pF H0:pM=pFH0:pM=pF H1:pM≠pFH1:pM≠pF H0:μM=μFH0:μM=μF H1:μM<μFH1:μM<μF H0:μM=μFH0:μM=μF H1:μM>μFH1:μM>μF H0:μM=μFH0:μM=μF H1:μM≠μFH1:μM≠μF The test is: two-tailed left-tailed right-tailed Based on a sample of 40 men, 30% owned cats Based on a sample of 20 women, 50% owned cats The test statistic is:  (to 2 decimals) The p-value...
Test the claim that the proportion of men who own cats is significantly different than the...
Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level. The null and alternative hypothesis would be: H 0 : p M = p F H 1 : p M ≠ p F H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M >...
Test the claim that the proportion of men who own cats is significantly different than 70%...
Test the claim that the proportion of men who own cats is significantly different than 70% at the 0.01 significance level. The null and alternative hypothesis would be: H0:μ=0.7H0μ0.7 H1:μ>0.7H1μ0.7 H0:p=0.7H0p0.7 H1:p>0.7H1p0.7 H0:p=0.7H0p0.7 H1:p<0.7H1p0.7 H0:p=0.7H0p0.7 H1:p≠0.7H1p0.7 H0:μ=0.7H0μ0.7 H1:μ≠0.7H1μ0.7 H0:μ=0.7H0μ0.7 H1:μ<0.7H1μ0.7 The test is: right-tailed left-tailed two-tailed Based on a sample of 25 people, 63% owned cats The test statistic is:  (to 2 decimals) The positive critical value is:  (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject...
1. Test the claim that the proportion of people who own cats is significantly different than...
1. Test the claim that the proportion of people who own cats is significantly different than 30% at the 0.2 significance level. The null and alternative hypothesis would be: a) H0:μ≤0.3 Ha:μ>0.3 b) H0:p≥0.3 Ha:p<0.3 c) H0:μ≥0.3 Ha:μ<0.3 d) H0:p≤0.3 Ha:p>0.3 e) H0:μ=0.3 Ha:μ≠0.3 f) H0:p=0.3 Ha:p≠0.3 The test is: -left-tailed -two-tailed -right-tailed Based on a sample of 400 people, 31% owned cats The p-value is: ____? (to 2 decimals) Based on this we: Reject the null hypothesis Fail to...
You are testing the claim that the proportion of men who own cats is significantly different...
You are testing the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats. You sample 160 men, and 20% own cats. You sample 80 women, and 35% own cats. Find the test statistic, rounded to two decimal places.
Test the claim that the proportion of men who own cats is smaller than the proportion...
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:pM=pFH0:pM=pF H1:pM<pFH1:pM<pF The test is: left-tailed Based on a sample of 20 men, 45% owned cats Based on a sample of 60 women, 70% owned cats The test statistic is: ___ (to 2 decimals) The p-value is: ____ (to 2 decimals)
Test the claim that the proportion of men who own cats is smaller than the proportion...
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: H 0 : p M = p F H0:pM=pF H 1 : p M ≠ p F H1:pM≠pF H 0 : μ M = μ F H0:μM=μF H 1 : μ M < μ F H1:μM<μF H 0 : p M = p F H0:pM=pF H 1...
Test the claim that the proportion of men who own cats is smaller than the proportion...
Test the claim that the proportion of men who own cats is smaller than the proportion of women who own cats at the .10 significance level. left tailed right tailed two tailed test statistic critical value reject or accept the null
Test the claim that the proportion of men who own cats is larger than 20% at...
Test the claim that the proportion of men who own cats is larger than 20% at the .05 significance level. The null and alternative hypothesis would be: H0:p=0.2H0:p=0.2 H1:p≠0.2H1:p≠0.2 H0:p=0.2H0:p=0.2 H1:p>0.2H1:p>0.2 H0:μ=0.2H0:μ=0.2 H1:μ≠0.2H1:μ≠0.2 H0:μ=0.2H0:μ=0.2 H1:μ<0.2H1:μ<0.2 H0:p=0.2H0:p=0.2 H1:p<0.2H1:p<0.2 H0:μ=0.2H0:μ=0.2 H1:μ>0.2H1:μ>0.2 The test is: right-tailed two-tailed left-tailed Based on a sample of 30 people, 29% owned cats The test statistic is:  (to 2 decimals) The critical value is:  (to 2 decimals) Based on this we: Reject the null hypothesis Fail to reject the null...
You are testing the claim that the proportion of men who own cats is smaller than...
You are testing the claim that the proportion of men who own cats is smaller than the proportion of women who own cats. You sample 180 men, and 75% own cats. You sample 120 women, and 15% own cats. Find the test statistic, rounded to two decimal places.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT