Introduction to Biostatistics Assessment Answer

Question 1 (12 marks)

a)

Step 1:

Null hypothesis: The population median difference is zero

Alternative hypothesis: The population median difference is not zero

Alpha = 0.05

The Sign test is will be used.

b) The number of observations is, the level of significance is and the alternate hypothesis is two-sided. Using the given table 6, the critical value is 1 at n =10 and alpha = 0.05

Reject null hypothesis if the smaller the number of plus signs or minus signs is.

Alternatively, we could use R Commander to calculate the p-value for this test and reject the null hypothesis if.

Compute the Test Statistic

The test statistics is the smaller of the number ‘more’ and the number ‘less’. As there are 3 ‘more’ and 7 ‘less’ the test statistic is 3.

Alternatively, we could use the relationship between the Sign test and the binomial distribution with to calculate the p-value for this test. The p-value is (as this is a two-sided test, we have doubled to result).

d)

As the test statistic (3) is greater than the critical value (1) there is insufficient evidence to reject the null hypothesis. Hence, the test does not provides evidence of a change in the drinking habits of the wider population of graduates from the University of Eastern Sydney.

Question 2 (6 marks)

a) The 95% confidence interval is (43.89, 44.83).

b) We are 95% confident that the true population mean well-being score will lie between 43.89 to 44.83.

Question 3 (5 marks)

• Would you address this research question with a one-tailed hypothesis test or a two-tailed hypothesis test? Explain why. (1 mark)

This is a one-tailed test as we are testing that drug users have lower well-being score than non-users. This is a left tailed test.

• Write the null and alternate hypotheses for a parametric hypothesis test, fully defining any symbols which you use. (2 marks)

Null hypothesis: The mean well-being score for drug users is same as non-users.

Alternative hypothesis: The mean will-being score for drug users is lower than non-users.

• Using the University of Eastern Sydney data set assigned to you and R Commander find and report (2 marks)

1. the mean wellbeing (WEMWBS) score for drug users in the sample
2. the mean wellbeing (WEMWBS) score for non-users in the sample

• the p-value for the difference in mean wellbeing (WEMWBS) between these two groups in the population

The mean well-being score for drug user is 43.88 and for non-user the score is 44.83.

The p-value for difference in mean wellbeing between these two groups is 0.0229.

• Based on the results of c) provide your answer to the research question. (2 marks)

Since, the p-value is less than level of significance 5%. Hence, null hypothesis is rejected and we conclude that the mean wellbeing score for drug users is lower than non-users.

Question 4 (7 marks)

a) Solution:

The alternative of the t-test conduct is Mann-Whitney U test.

The hypotheses are given as follows:

Step 1:

Null hypothesis: The median well-being score for drug users is same as non-users.

b) Alternative hypothesis: The median will-being score for drug users is lower than non-users.

c) The level of significance is 0.05. Reject the null hypothesis if p-value is less than 0.05.

d) The test-statistic value is W = 8299.5

e) The p-value is 0.0602.

Step 5:

Since, the p-value is greater than 5% level of significance. Hence, the null hypothesis is not rejected here.

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