Question

A chemist measures the haptoglobin concentration (in grams per litre) in the blood serum from a random sample of 11 healthy adults. The concentrations are assumed to be normally distributed and are given below.

1.4,1,1.8,1.8,0.4,1.5,2.2,0.8,0.9,3.3,2.2

At a 1% level of significance, perform a statistical test to see if there is evidence that the mean haptoglobin concentration in adults is less than 1.8 grams per litre, by answering the following parts.

1.1 (.8 marks)

Give the Null and Alternative Hypotheses, using mu to denote the population mean. H0 : 1.1.2 (.4 marks) HA : 1.2 (.2 marks) What's the significance level α? α =   1.3 (1 mark) Find the value of the test statistic correct to 2 decimal places. t ≈   1.4 (1 mark) What is the p-value? Give your answer to 3 decimal place accuracy. p-value ≈   You have not attempted this yet 1.5 (.5 marks) Is the p-value less than the critical value? You have not attempted this yet 1.6 (.5 marks) Should we reject H0?

Answer 1

:- Average haptoglobin concentration in adults

Number	Values (X)
1	1.4	0.0298
2	1	0.3280
3	1.8	0.0517
4	1.8	0.0517
5	0.4	1.3753
6	1.5	0.0053
7	2.2	0.3935
8	0.8	0.5971
9	0.9	0.4526
10	3.3	2.9835
11	2.2	0.3935
Total	17.3	6.6618

Mean   

Standard deviaition   

To Test :-

H₀ :-  

H₁ :-  

Test Statistic :-

t = -0.9236

Test Criteria :-

Reject null hypothesis if   

= 1% = 0.01

= -0.9236 > - 2.764, We fail to reject null hypothesis

Conclusion :- Accept Null Hypothesis

There is no sufficient evidence to conclude that there is statistically significance in average haptoglobin concentration in adults is less than 1.8.

Decision based on P value

P value using excel = 0.1887

Reject null hypothesis if P value < = 0.01 level of significance

0.1887 > 0.01, we fail to reject null hypothesis

conclusion :- Accept Null Hypothesis