BSB123 Data Analysis

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