QUESTION 1:
Based on your analysis, answer the following questions.
A. List errors in the following hypotheses: H0: P̂ > 0.20 and HA: P̂ ≥ 0.25
B. What is wrong with the following statement?
“If p-value is small we reject the null hypothesis and accept the alternative hypothesis.”
C. Identify a research question in a topic that interests you related to the concepts covered in this unit.
Define the population parameter and the statistics that will be used to conduct the inference on the population. State and explain the hypotheses.
Explain how you will collect the data and carry out a hypothesis test of the research question you have identified.
Draw a conclusion based on the hypothesis test you have described in the previous question.
D. If we want to decrease the margin of error, and hence have a more precise confidence interval, should we increase or decrease the sample size? Justify your answer with relevant examples.
REFERENCES:
Diez, D. M., Barr, C. D., & Çetinkaya-Rundel, M. (2019). Openintro statistics – Fourth edition. Open Textbook Library.
https://www.biostat.jhsph.edu/~iruczins/teaching/books/2019.openintro.statistics.pdf
• Read Chapter 5 – Foundations for Inference
o Section 5.3 – Hypothesis testing for a proportion from page 189 to page 205
• Read Chapter 6 – Inference for categorical data
o Section 6.1 – Inference for a single proportion from page 208 to page 217
o Section 6.2 – Difference of two proportions from page 217 to page 228
QUESTION 2:
This assignment will assess your knowledge and skill in interpreting the results of hypothesis testing for single and two proportions. Complete both Part 1 and Part 2.
Part 1
A group of 441 adults who did not have a college degree and were not currently enrolled in school were randomly selected. 38% of them said they did not attend college because they could not afford it.
For the given data:
a. Conduct a hypothesis test to determine if there is strong evidence supporting the statement that less than 50% of adults who decide not to attend college are because they cannot afford it. State the hypotheses and validate the independence and success-failure condition. Compute test statistic, and p-value, interpret the data, and conclude if the null hypothesis needs to be rejected or not.
b. Suppose we wanted the margin of error for the 90% confidence level to be about 1.5%. How large of a survey would you recommend?
Part 2
A random sample study was conducted on 13,270 Texas and 4,681 Dallas residents. It was found that the proportion of residents who reported insufficient rest or sleep during each of the preceding 31 days is 7.0% in Texas and 6.8% in Dallas.
a. Calculate a 95% confidence interval for the difference between the proportions of sleep-deprived individuals among Texas residents and Dallas residents. Explain the validation of independence and success-failure condition. Construct the interval and interpret it in the context of this study.
b. Conduct a hypothesis test to determine if the provided data is strong evidence for the rate of sleep deprivation is different for the two states given α = 0.05. Calculate the test statistics, and p-value and provide a conclusion to support your observation.
INSTRUCTION SUBMISSION
• Submit your submission in one document.
• Write the question number before your answer.
