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BSB123 Data Analysis

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  • Course Code: BSB123
  • University: Queensland University Of Technology
  • Country: Australia

Questions:

Q 1 

Explain the following terms clearly with an appropriate diagram where necessary

  1. Significance level
  2. Critical value
  3. P-value
  4. Type II error
  5. One tail hypothesis test

Q 2: 

  1. A research team wants to know if aspirin helps to thin blood. The null hypothesis says that it does not. They test 12 patients, observe the proportion with thinner blood, and get a p-value of 0.32. They proclaim that aspirin does not work. What would you say?

  2. A bank is testing a new method for getting delinquent customers to pay their past due credit card bills. The standard way was to send a letter (costing $0.40 each) asking the customer to pay. That worked 30% of the time. They want to test a new method that involves sending a video tape to the customer encouraging them to contact the bank and set up a payment plan. Developing and sending the video costs about $10.00 per customer. What is the parameter of interest? What are the null and alternate hypotheses?

  3. The bank sets up an experiment to test the effectiveness of the video tape. They mail it out to several randomly selected delinquent customers and keep track of how many actually do contact the bank to arrange payments. The banks statistician calculates the P-value of 0.003. What does this p-value suggest about the video tape?

  4. The statistician tells the ban’s management that the results are clear and that they should switch to the video tape method. Do you agree? What else may you also wish to know?

Q 3:

A tyre manufacturer is considering a new designed treat pattern for its all-weather tyres. Tests have indicated that these tyres provide better fuel economy and long tread life. The last remaining test is to measure the distance that it takes for a car to stop from 100km/h. They hope that the tyre will stop within 125 feet and will adopt the new tread pattern unless there is strong evidence that the tyres do not meet this objective. The distances (in feet) for 10 stops on a test track are

129, 128, 130, 132, 135, 123, 102, 125, 128, 130

  1. Should the company adopt the new tread pattern? Test an appropriate hypothesis and state your conclusion.

  2. Explain how you dealt with the outlier, and why you made the recommendation you did.
 

Answers:

Question One

  1. The significance level is an evaluation of the strength of proof that must exist in a statistical test to reject the null hypothesis and conclude that the alternative hypothesis is true. It is denoted as alpha, and the researcher must determine it before experimenting. The significance level is the likelihood of rejecting the null hypothesis when it is true(Kenton, 2020). For instance, at the 0.01 significance level, we have a 10% chance of concluding that a difference exists when there is no difference.

  2. The critical line refers to the line on a graph that separates the rejection area and the accepted area, as shown in the diagram below:

 

We reject the null hypothesis and consequently accept the alternative hypothesis if the test value falls in that region, else we accept the null hypothesis (Critical Values: Find a Critical Value in Any Tail, 2020). The above is a critical line for the one-tail test. A two-tail test has two lines symmetrically placed on both sides.

  1. P-value is the likelihood of obtaining the observed, or more extreme results when the null hypothesis of a test experiment is true. The p-value applies as an alternative to rejection points to give the smallest significance level where the null hypothesis should be rejected(Beers, 2020). The smaller the value, the stronger the evidence in favor of the alternative hypothesis.
  2. Type II error is the probability of failing to reject the null hypothesis when it is false—for instance, failing to reject the null hypothesis when the p-value is not less than the critical value(What are Type I and Type II Errors, 2019).
  3. One tail hypothesis test is a statistical test where the critical area of the distribution is one-sided, implying that it is either greater than or less than the critical value, but not both(Critical Values: Find a Critical Value in Any Tail, 2020). The alternative hypothesis will be accepted instead of the null hypothesis if the sample being tested falls into the one-sided critical area.

Question Two

  1. The p-value of 0.32 is not less than the appropriate significance level of 0.05; therefore, I fail to reject the null hypothesis that aspirin does not help to thin the blood.
  2. The parameter of interest is that the videotape method will work more than 30% of the time. The null hypothesis states that the videotape method will work less than or equal to 30% of the time, while the alternative hypothesis states that the videotape method will work more than 30% of the time.
  3. The p-value of 0.003 is significantly small; therefore, we reject the null hypothesis and conclude that the videotape method works more than 30% of the time.
  4. Yes, I agree and may wish to know the average percentage of time that the videotape method works.

 

Question Three

 a.

 

b. I did not remove the outlier since it lies within the alternative hypothesis.

 

 

References

Beers, B. (2020, February 19). P-Value Definition. Retrieved from Investopedia: https://www.investopedia.com/terms/p/p-value.asp

Critical Values: Find a Critical Value in Any Tail. (2020). Retrieved from Statistics how to: https://www.statisticshowto.com/probability-and-statistics/find-critical-values/

Kenton, W. (2020, January 27). Statistical Significance. Retrieved from Investopedia: https://www.investopedia.com/terms/s/statistically_significant.asp

What are Type I and Type II Errors? (2019, July 4). Retrieved from Simply Psychology: https://www.simplypsychology.org/type_I_and_type_II_errors.html

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