Introductory Biostatistics Assignment 2: Inference

Name: _______ ______________ ID number: ________________________
Introductory Biostatistics
Assignment 2: Inference
The population data
The population we are considering for this assignment are the 10,000
kuku (New Zealand green–lipped mussels) growing in a mussel farm in
the Marlborough Sounds.
For assignment 1 you obtained data on a sample of 100 randomly
selected kuku. You will use the data from this same sample for
Assignment 2.
The variables of interest are the length of the kuku (in millimetres), grade (small, medium or large)
and sex (male or female)
Part A: Confidence Interval for a proportion [12 marks]
1. What is the proportion of kuku that are female in your sample? [1 mark]
The proportion of kuku that are female in my sample is 0.5 expressed as percentage is 50%
2. Confidence interval [8 marks]
Construct and interpret a 95% confidence interval for the proportion of kuku in the Marlborough Sounds
mussel farm that are female.
You MUST show your working to get full marks.
General formula for a CI:
Sample size = 100
Statistic = Proportion = 0.5
Standard Error = SE= √ P (1−P)
n = √ 0.5( 1−0.5)
100 =0.05
Critical value = For 95% confidence level (0.05 significance level) critical value is
1.9600
Interval half width = ME=SE∗Z value=(0.05 x 1.96=0.098)
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Name: _______ ______________ ID number: ________________________
95% CI = 0.5−0.098=0.402 and 0.5+0.098=0. 598
95 % CI =0.402 ≤ P ≤ 0.598
Interpretation: At 95% level of confidence, the proportion of kuku’s that are female
range from between 0.402 to 0.598.
3. Validity of the confidence interval [3 marks]
Is the confidence interval valid? (i.e. Are the conditions for the confidence interval satisfied?)
When the confidence interval of proportion is being calculated. The following conditions
must hold:
 The sample must be collected through random sampling.
 The data in the sample must be independent of each other
 Sample drawn without replacement, sample size should not be more than 10% of
the population
 The sample size must be relatively large.
In this scenario, we that all the above conditions have been satisfied and therefore the
confidence interval is valid.
Part B: Hypothesis test for a proportion [19 marks]
The farmer has been told that the survival of a mussel farm is threatened if more than 25% of the kuku are
male. You are to carry out a hypothesis test using the data from your sample to decide if the farmer should
be concerned about the survival of his Marlborough Sounds mussel farm.
1. Explain why a one-sided test is appropriate for this situation. [1 mark]
One-sided hypothesis test is more appropriate in this scenario because we are to
conduct a test on whether there are strictly more than 25% of male kuku’s in the farm
and disregard the existence of less than 25% male kuku’s in the farm. In other words,
we can say that an extreme value on the upper tail of the distribution of the male kuku
would cause the farmer to reject the null hypothesis
2. State the null and alternative hypotheses for this test in words and symbols. [3 marks]
H0 P≥0.25 Proportion of Male Kuku’s is greater than or equal to 25%
H1: P<0. 25 Proportion of Male Kuku’s is less than 25%
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