 # 1. You are performing a two-tailed test with test statistic z=&minu...

## Question

1. You are performing a two-tailed test with test statistic z=−0.3, find the p-value to 4 decimal places.

2. You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.14. Thus you are performing a right-tailed test. Your sample data produce the test statistic z=3.017. Find the p-value accurate to 4 decimal places.

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 less than 38%. With H1 : p < 38% you obtain a test statistic of z=−1.585. Find the p-value accurate to 4 decimal places.

p-value = ?

4. Testing:
H0:p=0.84
H1:p>0.84

Your sample consists of 107 subjects, with 91 successes. Calculate the test statistic, rounded to 2 decimal places
z= ?

5.
In a recent Super Bowl, a TV network predicted that 66 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 56 people who saw the commercials and found that 40 of them said they would watch one of the television shows.

Suppose you are have the following null and alternative hypotheses for a test you are running:
H0:p=0.66
Ha:p≠0.66

Calculate the test statistic, rounded to 3 decimal places
z=?

6. You are conducting a study to see if the probability of catching the flu this year is significantly more than 0.6. You use a significance level of α=0.10.
H0:p=0.6
H1:p>0.6

You obtain a sample of size n=389 in which there are 258 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 = ?

7.
Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 250 times and got 104 heads. We wish to find how significant is this evidence against equal probabilities.

What is the sample proportion of heads?
Round to 3 places.
Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different?

8. 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 50 stocks traded on the NYSE that day showed that 21 went up.

You are conducting a study to see if the proportion of stocks that went up is is significantly more than 0.3. You use a significance level of α=0.01.

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 =

9. Testing:

H0:μ=47.14
H1:μ≠47.14

Your sample consists of 39 subjects, with a mean of 49.3 and standard deviation of 4.72.
Calculate the test statistic, rounded to 2 decimal places.
t= ?

10. You wish to test the following claim (Ha) at a significance level of α=0.05.
Ho:μ=75.8
Ha:μ≠75.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=14 with mean M=70.3 and a standard deviation of SD=18.8.

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 = ?

11. You wish to test the following claim (Ha) at a significance level of α=0.10.
Ho:μ=70.2
Ha:μ>70.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=57 with mean M=78 and a standard deviation of SD=14.7.

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 =

## Solution Preview

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1. You are performing a two-tailed test with test statistic z=−0.3, find the p-value to 4 decimal places.
Solution:
Here we need to find
P(Z>0.3) or P(Z<-0.3)
=1-2*P(0<Z<0.3)
= 0.764177
The answer to 4 decimal places is 0.7642

2. You are conducting a study to see if the proportion of voters who prefer Candidate A is significantly more than 0.14. Thus you are performing a right-tailed test. Your sample data produce the test statistic z=3.017. Find the p-value accurate to 4 decimal places.
p-value = ?
Solution:
Here we need to find
P(Z>3.017)
=0.5-P(0<Z<3.017)
The P-Value is 0.001276
The answer to 4 decimal places is 0.0013...

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