1.A well-known brokerage firm executive claimed that 20% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 500 people, 135 of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 20% at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:=0.2

H1:<0.2

H0:p=0.2

H1:p<0.2

H0:=0.2

H1:>0.2

H0:p=0.2

H1:p0.2

H0:p=0.2

H1:p>0.2

H0:=0.2

H1:0.2

The test is:

left-tailed

right-tailed

two-tailed

The test statistic is:(to 3 decimals)

The p-value is:(to 4 decimals)

Based on this we:

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

2.Test the claim that the proportion of people who own cats is significantly different than 20% at the 0.2 significance level.

The null and alternative hypothesis would be:

H0:p=0.2

H1:p<0.2

H0:p=0.2

H1:p>0.2

H0:p=0.2

H1:p0.2

The test is:

two-tailed

left-tailed

right-tailed

Based on a sample of 300 people, 27% owned cats

The p-value is:(to 2 decimals)

Based on this we:

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

3.You wish to test the following claim (HaHa) at a significance level of =0.001

Ho:p1=p2

Ha:p1p2

You obtain a sample from the first population with 389 successes and 56 failures (Note: You will have to calculate the total sample size by adding the number of successes and failures).

You obtain a sample from the second population with 586 successes and 65 failures (Note: You will have to calculate the total sample size by adding the number of successes and failures).

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

test statistic =

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

p-value =

The p-value is...

• less than (or equal to)
• greater than

This test statistic leads to a decision to...

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

As such, the final conclusion is that...

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

4.You wish to test the following claim (HaHa) at a significance level of =0.001

Ho:p1=p2

Ha:p1p2

You obtain a sample from the first population with 389 successes and 56 failures (Note: You will have to calculate the total sample size by adding the number of successes and failures).

You obtain a sample from the second population with 586 successes and 65 failures (Note: You will have to calculate the total sample size by adding the number of successes and failures).

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

test statistic =

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

p-value =

The p-value is...

• less than (or equal to)
• greater than

This test statistic leads to a decision to...

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

As such, the final conclusion is that...

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