Question

1.) Two samples are taken with the following numbers of successes and sample sizes
r1 = 35 r2 = 34
n1 = 92 n2 = 72

Find a 99% confidence interval, round answers to the nearest thousandth.
< p1−p2 <

2.)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:

a.)

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

B.)The test is:

-left-tailed

-right-tailed

-two-tailed

Based on a sample of 40 men, 25% owned cats
Based on a sample of 60 women, 30% owned cats

C.) The test statistic is: (to 2 decimals) _____
D.) The p-value is: (to 2 decimals) _______

E.) Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

3. (Note: I have done this problem several times with different numbers and can not seem to get all of them correct. Could you please show your work and if you use a calculator(TI83+) please show how you entered it in. My class does not look at charts, they use the calculators which is very confusing to me.)

Test the claim that the proportion of children from the low income group that drew the nickel too large is greater than the proportion of the high income group that drew the nickel too large. Test at the 0.1 significance level.

26 of 40 children in the low income group drew the nickel too large, and 16 of 35 did in the high income group.

a) If we use L to denote the low income group and H to denote the high income group, identify the correct alternative hypothesis.

H1:μL>μH

H1:μL≠μH

H1:pL<pH

H1:pL>pH

H1:pL≠pH

H1:μL<μH
b) The test statistic value is (two decimal places):
c) Using the P-value method, the P-value is (4 decimal places):

d) Based on this, we...

Reject H0

• Fail to reject H0

e) Which means

• There is not sufficient evidence from the sample data to support the claim
• The sample data supports the claim
• There is not sufficient evidence from the sample data to warrant rejection of the claim
• There is sufficient evidence from the sample data to warrant rejection of the claim

4.) (Note:I got partial credit for this answer but am unsure of what the other ones are)

A student was asked to find a 90% confidence interval for the proportion of students who take notes using data from a random sample of size n = 89. Which of the following is a correct interpretation of the interval 0.14 < p < 0.35?

Check all that are correct.

There is a 90% chance that the proportion of the population is between 0.14 and 0.35.
With 90% confidence, a randomly selected student takes notes in a proportion of their classes that is between 0.14 and 0.35.
There is a 90% chance that the proportion of notetakers in a sample of 89 students will be between 0.14 and 0.35.
With 90% confidence, the proportion of all students who take notes is between 0.14 and 0.35.
The proportion of all students who take notes is between 0.14 and 0.35, 90% of the time.

5.) (Note: Need help with a.) & e.) )

You wish to test the following claim (Ha) at a significance level of α=0.005.

      Ho:p1=p2
      Ha:p1<p2

You obtain 156 successes in a sample of size n1=542 from the first population. You obtain 171 successes in a sample of size n2=454 from the second population.

a.)What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

b.)What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

c.)The p-value is...
less than (or equal to) α
greater than α

d.)This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

e.)As such, the final conclusion is that...

There is sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
There is not sufficient evidence to warrant rejection of the claim that the first population proportion is less than the second population proportion.
The sample data support the claim that the first population proportion is less than the second population proportion.
There is not sufficient sample evidence to support the claim that the first population proportion is less than the second population proportion.

Answer 1

r1 = 35, n1 = 92
r2 = 34, n2 = 72

Sample proportions:

(Round to 4 decimal)

(Round to 4 decimal)

99% confidence interval is

where SE is standard error

(Round to 4 decimal)

where zc is z critical value for (1+c)/2 = (1+0.99)/2 = 0.995 is

zc = 2.58 (From statistical table of z values)

(Round to 3 decimal)

99% confidence interval is (-0.292, 0.108)