Question

1. A random survey of 400 people provided the following information about what sports they watch on television: 21% watched soccer, 43% watched football, and 56% watched soccer or football.

The events watching soccer and watching football are:

a. Mutually exclusive and independent.

b. Independent only.

c. Mutually exclusive only.

d. Neither mutually exclusive nor independent.

2. A random survey of 400 people provided the following information about what sports they watch on television: 21% watched soccer, 43% watched football, and 56% watched soccer or football.

What percent of the surveyed people watched both soccer and football?

a. 64%

b. 44%

c. 56%

d. 8%

3. Suppose a major manufacturer claims that less than 6% of its fax machines are defective.

It tests a random sample of 280 fax machines and finds that 14 are defective.

A Type I error would be to conclude that

a. at least 6% of its fax machines are defective, when in fact the proportion is less than 6%.

b. 6% of its fax machines are defective when in reality the proportion is 5%.

c. less than 6% of its fax machines are defective, when in fact the proportion is at least 6%.

d. 6% of its fax machines are defective when in reality the proportion is not 6%.

4. Suppose a major manufacturer claims that less than 6% of its fax machines are defective.

It tests a random sample of 280 fax machines and finds that 14 are defective.

The p-value is the probability of getting a sample proportion of

a. 0.06 or greater, if the null hypothesis is true and the population proportion is 0.05

b. less than 0.06, if the null hypothesis is true and the population proportion is 0.06

c. 0.06 or greater, if the null hypothesis is true and the population proportion is 0.06

d. 0.05 or less, if the null hypothesis is true and the population proportion is 0.06

5. Suppose a major manufacturer claims that less than 6% of its fax machines are defective.

It tests a random sample of 280 fax machines and finds that 14 are defective.

What kind of test is this?

a. Test of single proportion

b. Test of 2 means

c. Test of single mean

d. Test of 2 proportions

6. Suppose a major manufacturer claims that less than 6% of its fax machines are defective.

It tests a random sample of 280 fax machines and finds that 14 are defective.

Which conclusion is most appropriate at the 3% level of significance?

a. At least 6% of the fax machines are defective.

b. 5% or more of the fax machines are defective.

c. Less than 6% of the fax machines are defective.

d. At most 6% of the fax machines are defective.

Answer 1

#1.
P(S and F) = 0.21 + 0.43 - 0.56 = 0.08

P(S) * P(F) not equals to P(S and F)
hence not independent.

Option D

#2.
P(S and F) = 0.21 + 0.43 - 0.56 = 0.08

option D

#3.
less than 6% of its fax machines are defective, when in fact the proportion is at least 6%.

option C

#4.
less than 0.06, if the null hypothesis is true and the population proportion is 0.06
option B

#5.
Test of single proportion

Option A

#6.
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.06
Alternative Hypothesis, Ha: p < 0.06

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.05 - 0.06)/sqrt(0.06*(1-0.06)/280)
z = -0.7

P-value Approach
P-value = 0.242
As P-value >= 0.03, fail to reject null hypothesis.

a. At least 6% of the fax machines are defective.

Option A