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Stats easy HW questions

Stats easy HW questions

Daniel Kevins

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**They are mostly multiple choice ***

1. Test the claim that the proportion of people who own cats is smaller than 30% at the 0.025 significance level.

The null and alternative hypothesis would be:

The test is:

right-tailed

left-tailed

two-tailed

Based on a sample of 800 people, 26% owned cats

The p-value is:

(to 2 decimals)

2. A well-known brokerage firm executive claimed that 60% 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 600 people, 66% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 60% at the 0.10 significance level.

The null and alternative hypothesis would be:

The test is:

two-tailed

left-tailed

right-tailed

The test statistic is:

(to 3 decimals)

The p-value is:

(to 4 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

Past studies have indicated that the percentage of smokers was estimated to be about 30%. Given the new smoking cessation programs that have been implemented, you now believe that the percentage of smokers has reduced. You randomly surveyed 1884 people and found that 520 smoke. Use a 0.05 significance level to test the claim that the percentage of smokers has reduced.

a) Identify the null and alternative hypotheses?

$H_{0}$

$H_{0}$ :

$H_{1}$

$H_{1}$ :

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

left-tailed
right-tailed
two-tailed

c) Identify the appropriate significance level.

d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.

e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.

f) Do you reject the null hypothesis?

We reject the null hypothesis, since the p-value is less than the significance level.
We reject the null hypothesis, since the p-value is not less than the significance level.
We fail to reject the null hypothesis, since the p-value is less than the significance level.
We fail to reject the null hypothesis, since the p-value is not less than the significance level.

g) Select the statement below that best represents the conclusion that can be made.

There is sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 30%.
There is not sufficient evidence to warrant rejection of the claim that the percentage of smokers is less than 30%.
The sample data support the claim that the percentage of smokers is less than 30%.
There is not sufficient sample evidence to support the claim that the percentage of smokers is less than 30%

4. You are concerned that nausea may be a side effect of Tamiflu, but you cannot just give Tamiflu to patients with the flu and say that nausea is a side effect if people become nauseous. This is because nausea is common for people who have the flu. From past studies you know that about 34% of people who get the flu experience nausea. You collected data on 2119 patients who were taking Tamiflu to relieve symtoms of the flu, and found that 780 experienced nausea. Use a 0.01 significance level to test the claim that the percentage of people who take Tamiflu for the relief of flu symtoms and experience nausea is greater than 34%.

a) Identify the null and alternative hypotheses?

$H_{0}$

$H_{0}$ :

$H_{1}$

$H_{1}$ :

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

left-tailed
right-tailed
two-tailed

c) Identify the appropriate significance level.

d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.

e) Calculate your p-value. Write the result below, and be sure to round your final answer to four decimal places.

f) Do you reject the null hypothesis?

We reject the null hypothesis, since the p-value is less than the significance level.
We reject the null hypothesis, since the p-value is not less than the significance level.
We fail to reject the null hypothesis, since the p-value is less than the significance level.
We fail to reject the null hypothesis, since the p-value is not less than the significance level.

g) Select the statement below that best represents the conclusion that can be made.

There is sufficient evidence to warrant rejection of the claim that the percentage of people who experience nausea is greater than 34%.
There is not sufficient evidence to warrant rejection of the claim that the percentage of people who experience nausea is greater than 34%.
The sample data support the claim that the percentage of people who experience nausea is greater than 34%
There is not sufficient sample evidence to support the claim that the percentage of people who experience nausea is greater than 34%

h) Can we conclude that nausea a side effect of Tamiflu?

Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.

A sample of 57 stocks traded on the NYSE that day showed that 7 went up.

You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of $α = 0.10$

$α = 0.10$ .

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

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

The p-value is…

less than (or equal to) $α$
greater than $α$

This p-value 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 proportion of stocks that went up is is less than 0.3.
There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is is less than 0.3.
The sample data support the claim that the proportion of stocks that went up is is less than 0.3.
There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is is less than 0.3.

6. 6.16 Is college worth it? Part I: Among a simple random sample of 331 American adults who do not have a four-year college degree and are not currently enrolled in school, 48% said they decided not to go to college because they could not afford school.

(a) A newspaper article states that only a minority of the Americans who decide not to go to college do so because they cannot afford it and uses the point estimate from this survey as evidence. Conduct a hypothesis test to determine if these data provide strong evidence supporting this statement.
The hypotheses for this test are:

Ho: p = .5
Ha: p > .5
Ho: p = .5
Ha: p ≠ .5
Ho: p = .5
Ha: p < .5

The test statistic is: (please round to two decimal places) The p-value associated with this hypothesis test is: (please round to four decimal places) What is the conclusion of the hypothesis test?

Since p<α we fail to reject the null hypothesis
Since p<α we reject the null hypothesis and accept the alternative
Since p ≥ α we reject the null hypothesis and accept the alternative
Since p ≥ α we accept the null hypothesis
Since p ≥ α we do not have enough evidence to reject the null hypothesis

Interpret the result of the test in the context of this study and article:

The data provide sufficient evidence to claim that only a minority of Americans who choose not to go to college do so because they cannot afford it
The data do not provide sufficient evidence to claim that only a minority of Americans who choose not to go to college do so because they cannot afford it

(b) Would you expect a confidence interval for the proportion of American adults who decide not to go to college because they cannot afford it to include 0.5?

“Trydint” bubble-gum company claims that 3 out of 10 people prefer their gum to “Eklypse” and they want to test if this value is different.

The null and alternative hypothesis in symbols would be:

$H_{0} : p = 0.3$
$H_{1} : p \neq 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ \neq 0.3$
$H_{0} : p = 0.3$
$H_{1} : p > 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ < 0.3$
$H_{0} : p = 0.3$
$H_{1} : p < 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ > 0.3$

The null hypothesis in words would be:

The average of people that prefer Trydint gum is 0.3.
The average of people that prefer Trydint gum is not 0.3.
The proportion of people in a sample that prefers Trydint gum is 0.3.
The proportion of all people that prefer Trydint gum is less than 0.3.
The proportion of all people that prefer Trydint gum is greater than 0.3.
The proportion of people in a sample that prefer Trydint gum is not 0.3
The proportion of all people that prefer Trydint gum is 0.3

Based on a sample of 310 people, 91 said they prefer “Trydint” gum to “Eklypse”.

The point estimate is:

(to 3 decimals)

The 95 % confidence interval is:

to (to 3 decimals)

Based on this we:

Reject the null hypothesis
Fail to reject the null hypothesis

“Trydint” bubble-gum company claims that 3 out of 10 people prefer their gum to “Eklypse”. Test their claim that it is different at the 95 confidence level.

The null and alternative hypothesis in symbols would be:

$H_{0} : p = 0.3$
$H_{1} : p < 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ \neq 0.3$
$H_{0} : p = 0.3$
$H_{1} : p \neq 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ > 0.3$
$H_{0} : p = 0.3$
$H_{1} : p > 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ < 0.3$

The null hypothesis in words would be:

The proportion of all people that prefer Trydint gum is greater than 0.3.
The proportion of all people that prefer Trydint gum is 0.3
The proportion of people in a sample that prefers Trydint gum is 0.3.
The proportion of all people that prefer Trydint gum is less than 0.3.
The average of people that prefer Trydint gum is not 0.3.
The average of people that prefer Trydint gum is 0.3.
The proportion of people in a sample that prefer Trydint gum is not 0.3

Based on a sample of 180 people, 25 said they prefer “Trydint” gum to “Eklypse”.

The point estimate is:

(to 3 decimals)

The 95 % confidence interval is:

to (to 3 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

“Trydint” bubble-gum company claims that 3 out of 10 people prefer their gum to “Eklypse” and they want to test if this value is different.

The null and alternative hypothesis in symbols would be:

$H_{0} : p = 0.3$
$H_{1} : p \neq 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ \neq 0.3$
$H_{0} : p = 0.3$
$H_{1} : p > 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ < 0.3$
$H_{0} : p = 0.3$
$H_{1} : p < 0.3$
$H_{0} : μ = 0.3$
$H_{1} : μ > 0.3$

The null hypothesis in words would be:

The average of people that prefer Trydint gum is 0.3.
The average of people that prefer Trydint gum is not 0.3.
The proportion of people in a sample that prefers Trydint gum is 0.3.
The proportion of all people that prefer Trydint gum is less than 0.3.
The proportion of all people that prefer Trydint gum is greater than 0.3.
The proportion of people in a sample that prefer Trydint gum is not 0.3
The proportion of all people that prefer Trydint gum is 0.3

Based on a sample of 310 people, 91 said they prefer “Trydint” gum to “Eklypse”.

The point estimate is:

(to 3 decimals)

The 95 % confidence interval is:

to (to 3 decimals)

Based on this we:

Reject the null hypothesis
Fail to reject the null hypothesis

10.

Suppose the confidence interval (0.6358, 0.7532) represents the proportion of Skyline College students who say math is their favorite subject.

a. Based on the confidence interval, is it likely 60% of Skyline College students say math is their favorite subject?

Yes, all the interval values are greater than 0.60
Yes, 0.60 is not contained in the interval
No, 0.60 is not contained in the interval

Incorrectb. Based on the confidence interval, does it appear that more than 60% of Skyline College students say math is their favorite subject?

No, 0.60 is not contained in the interval
Yes, 0.60 is not contained in the interval
Yes, all the interval values are greater than 0.60

Incorrect
c. Based on the confidence interval, does it appear that fewer than 60% of Skyline College students say math is their favorite subject?

Yes, all the interval values are greater than 0.60
No, 0.60 is not contained in the interval
No, all the interval values are greater than 0.60

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Daniel Kevins

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