Question

Sonic Boom (SB) has a 34%-share of the CD market in San Geronimo. The company thinks an aggressive ad campaign would boost their share of the market. At the end of the ad campaign, SB conducts a survey of 100 CD buyers to determine the effect of the campaign with the result that 43 persons surveyed, bought their CD’s at SB. Is this sufficient evidence at the 5% level of significance to indicate that the ad campaign increased SB’s share of the market?

1. Based on this evidence one concludes at the 5% level of significance that the Sonic boom has:

a. 34% of the market share

b. 43% of the market share

c. more than 34% of the market share

d. less than 34% of the market share

e. none of these

2. The probability that a hypothesis test ends in a decision to accept a defective product is:

a. the producer’s risk

b. the consumer’s risk

c. the law of averages

d. a Type II error

e. a Type I error

3. When testing the null hypothesis, if you reject Ho, then ___________.

a. a Type I error was made

b. a Type II error is not made

c. Ho is false

d. Ho is true

e. None of these

4. When one accepts a true null hypothesis, one makes a _____________.

a. a Type II error

b. a Type I error

c. a correct decision

d. a and b

Answer 1

1)

Answer: c. more than 34% of the market share

Explanation:

The population proportion, p = 0.34

To test whether there is significant difference in results from survey, the z test for the one proportion is used since the sample data values satisfy the normality condition $np\geq10$

The null and alternative hypotheses are defined as,

$H_0:p=0.34$

$H_A:p>0.34$

The z-statistic is obtained using the formula,

$z=\frac{p-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$

$z=\frac{0.43-0.34}{\sqrt{\frac{0.34(1-0.34)}{100}}}=1.9$

The p-value is obtained from z-distribution table for z = 1.9

$\text{P-value}=0.0287$

Since the P-value is 0.0287<0.05 at 5% significant level, the null hypothesis is rejected hence we can conclude that the Sonic boom has more than 34% of the market share

2)

Answer: b. the consumer’s risk

Explanation: The probability of accepting the defecting product is known as the consumer’s risk

3)

Answer: c. Ho is false

Explanation: Rejecting the null hypothesis means the null hypothesis False.

4)

Answer: c. a correct decision

Explanation: If the null hypothesis is true and we accept the null hypothesis then it is a correct decision (and if reject the null hypothesis when it is true, it will be a type I error)