# 7.2 HW Hypothesis tests, Proportions 10 QUESTIONS 2

1. You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly more than 0.25.With H1 : p >> 0.25 you obtain a test statistic of z=1.397z=1.397.Use a normal distribution calculator and the test statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.

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2. You are conducting a study to see if the probability of catching the flu this year is significantly more than 0.27.With H1 : p >> 0.27 you obtain a test statistic of z=1.722z=1.722.Use a normal distribution calculator and the test statistic to find the P-value accurate to 4 decimal places. It may be left-tailed, right-tailed, or 2-tailed.

P-value =
3. You are conducting a study to see if the probability of a true negative on a test for a certain cancer is significantly more than 0.81. You use a significance level of α=0.001α=0.001.

H0:p=0.81H0:p=0.81 H1:p>0.81H1:p>0.81

You obtain a sample of size n=218n=218 in which there are 184 successes.

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…

a) less than (or equal to) αα
b) greater than αα

This test statistic leads to a decision to…

a) reject the null
b) accept the null
c) fail to reject the null

As such, the final conclusion is that…

a) There is sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is more than 0.81.
b)There is not sufficient evidence to warrant rejection of the claim that the probability of a true negative on a test for a certain cancer is more than 0.81.
c)The sample data support the claim that the probability of a true negative on a test for a certain cancer is more than 0.81.
d)There is not sufficient sample evidence to support the claim that the probability of a true negative on a test for a certain cancer is more than 0.81.

4. You are conducting a study to see if the proportion of men over 50 who regularly have their prostate examined is significantly different from 0.23. You use a significance level of α=0.02α=0.02.

H0:p=0.23H0:p=0.23 H1:p≠0.23H1:p≠0.23

You obtain a sample of size n=167n=167 in which there are 32 successes.

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…

A) less than (or equal to) αα
B) greater than αα

This test statistic leads to a decision to…

A)reject the null
B)accept the null
C)fail to reject the null

As such, the final conclusion is that…

A) There is sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.23.
B) There is not sufficient evidence to warrant rejection of the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.23.
C) The sample data support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.23.
D) There is not sufficient sample evidence to support the claim that the proportion of men over 50 who regularly have their prostate examined is different from 0.23.

5. 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 75 stocks traded on the NYSE that day showed that 26 went up.

You are conducting a study to see if the proportion of stocks that went up is significantly more than 0.3. You use a significance level of α=0.001α=0.001.

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…

A) less than (or equal to) αα
B) greater than αα

This test statistic leads to a decision to…

A) reject the null
B) accept the null
C) fail to reject the null

As such, the final conclusion is that…

A)There is sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3.
B)There is not sufficient evidence to warrant rejection of the claim that the proportion of stocks that went up is more than 0.3.
C)The sample data support the claim that the proportion of stocks that went up is more than 0.3.
D)There is not sufficient sample evidence to support the claim that the proportion of stocks that went up is more than 0.3.

6. 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 400 people, 54% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 60% at the 0.005 significance level.

The null and alternative hypothesis would be:
A) H0:p≥0.5H0:p≥0.5H1:p.50p>.50
C)    μ.50
F)    p0.7
B)   H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7
C)    H0:μ≤0.7H0:μ≤0.7H1:μ>0.7H1:μ>0.7
D)   H0:μ≥0.7H0:μ≥0.7H1:μ