1. A quality control manager thinks that there is a higher defective rate on the
ID: 3239501 • Letter: 1
Question
1. A quality control manager thinks that there is a higher defective rate on the production line than the advertised value of p = 0.025. She does a hypothesis test with a significance level of 0.05. Symbolically, the null and alternative hypothesis are as follows: H0: p = 0.025 and Ha: p > 0.025. She calculates a p-value for the hypothesis test of defective light bulbs to be approximately 0.067.
Choose the correct interpretation for the p-value.
Select one:
a. The p-value tells us that the probability of concluding that the defect rate is equal to 0.025, when in fact it is greater than 0.025, is approximately 0.067.
b. The p-value tells us that the result is significantly higher than the advertised value using a significance level of 0.05.
c. The p-value tells us that the true population rate of defective light bulbs is approximately 0.067.
d. The p-value tells us that if the defect rate is 0.025, then the probability that she would observe the percentage she actually observed or higher is 0.067. At a significance level of 0.05, this would not be an unusual outcome.
2. A researcher conducts a hypothesis test on a population proportion. Her null and alternative hypothesis are H0 : p = 0.4 and Ha : p < 0.4 . The test statistic and p-value for the test are z = ?3.01 and p?value = 0.0013 .
For a significance level of ? = 0.05 , choose the correct conclusion regarding the null hypothesis.
Select one:
a. There is sufficient evidence to conclude that the population proportion is significantly less than 0.4.
b. There is not sufficient evidence to conclude that the population proportion is significantly less than 0.4.
c. There is not sufficient evidence to reject the null hypothesis that the population proportion is equal to 0.4.
d. There is sufficient evidence to accept the null hypothesis that the population proportion is equal to 0.4.
3. A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest.
State the hypotheses to be tested for this study.
Select one:
a. H0: p = 0.16; Ha: p =? 0.16
b. H0: p =? 0.16; Ha: p < 0.16
c. H0: p = 0.16; Ha: p > 0.16
d. H0: p = 0.16; Ha: p < 0.16
4. A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest.
Check that the conditions hold so that the sampling distribution of the z-statistic will approximately follow the standard normal distribution. Are the conditions satisfied? If not, choose the condition that is not satisfied.
Select one:
a. No, the population of interest is not large enough to assume independence.
b. No, the researcher did not collect a random sample.
c. Yes, all the conditions are satisfied.
d. No, the researcher did not collect a large enough sample.
5. A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest.
A researcher completes a hypothesis test with a resulting p-value = 0.076. Choose the best statement to interpret the results.
Select one:
a. The p-value is above a standard cutoff value of ? = 0.05 and therefore there is sufficient evidence to support that the city of interest has a different proportion of smokers than the general public.
b. The p-value for a two-sided test is divided by 2 resulting in a value less than a standard cutoff value of ? = 0.05 supporting the hypothesis that the city of interest has a different proportion of smokers than the general public.
c. The p-value is above a standard cutoff value of ? = 0.05 and therefore there is insufficient evidence to support that the city of interest has a different proportion of smokers than the general public.
d. The standard cutoff value of ? = 0.05 is multiplied by two for a two-sided test and the resulting value of 0.10 is greater than the p-value. Therefore there is no evidence to support that the city of interest has a different proportion of smokers than the general public.
Explanation / Answer
#1 The correct option is:
d.
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#2 The correct option is:
a.
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#3 The correct option is:
a.
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#4 The correct option is:
c.
because np=75(0.16)=12 and n(1-p)=75(1-0.16)=63, both are atleast 10. Sample is random.
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#5 The correct option is:
c.
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