Question

1.

a. How large should the random sample of ink cartridges be so that at 92% confidence interval, the maximum allowable error between the estimate obtained from the sample and the true population mean is within 0.1mm. Previous studies have indicated that the standard deviation of the lengths of the cartridges produced to be 2mm.​ 6 marks

A sample of 400 Health statistics students taking a nationwide licensure examination revealed that an average score of 560 and a sample standard deviation of 100. What is the 99% confidence interval for the population mean?

​​​​​​ 9 marks

2.

a. The following data gives the experience of x–ray machine operators and their performance ratings as given by the number of quality x–ray pictures that turned out of 100 pieces.

Experience

16

12

18

4

3

10

5

12

Performance Ratings

87

88

89

68

78

80

75

83

As the Health Statistician of the clinic you have been asked to explain the relationship between these two variables

i. Use a scatter plot to explain the strength of relationship between the variables. 5 marks

ii. Using the data establish the regression model ​​ 10 marks

iii. How will you convince your Director that this model you have given is good enough to make predictions? ​​​​​​​​ 15 marks

3. 60 children were asked as to which ice cream flavour they liked out of the three flavours of vanilla, strawberry and chocolate and their answers were recorded as follows:

Flavour

Number of children

Vanilla 17

Strawberry 24

Chocolate 19

Determine whether children favour any particular flavour compared to the other flavours.

​​​​​​​​​15 marks

Answer 1