Question

Exercise 5

For the study in Exercise 4, DNA samples were taken from dingoes in different states

in Australia. In the state of Queensland, 356 samples were collected and 71 were

found to be purebred. In the state of South Australia, 148 samples were collected

and 47 were purebred.

(a) Estimate the difference in the proportion of dingoes that are purebred between

Queensland and South Australia. Be sure to use the appropriate method based on

the number of observations with and without the characteristic of interest.

(b) Calculate a 90% confidence interval for the difference in the proportion of purebred

dingoes between Queensland and South Australia. Be sure to use the appropriate

method based on the number of observations with and without the characteristic of

interest.

(c) Interpret the interval from Part (b) in words. Do you think there is a difference in

the proportion of purebred dingoes between Queensland and South Australia? Why

or why not?

Answer 1

Exercise 5

In Queensland, 71 out of 356 samples are purebred

In South Australia, 47 out of 148 samples were purebred

n₁ = 356

n₂ = 148

a)

Proportion of dingoes in Queensland (p₁) = 71/356 = 19.94%

Proportion of dingoes in South Australia (p₂) = 47/148 = 31.75%

Difference between proportion of dingoes in Queensland and South Australia

= p₁ – p₂

= 19.94% - 31.75%

= -11.81%

Thus, it is estimated that the proportion of purebred dingoes in Queensland is less than the proportion of purebred dingoes in South Australia by 11.81%

b)

Conducting inference from the difference in proportions as it is a random sample that can be divided into two and interpreted independently.

Confidence interval is given as:

• (p₁ – p₂) ± z* √ [p₁(1 - p₁)/ n₁ + p₁(1 - p₁)/ n₁] using z value for 90% confidence interval
• -0.1181 ± 1.645 * √ (0.00191183)
• -0.1181 ± 1.645 * 0.0437
• -0.1181 ± 0.07192
• (-0.19, -0.04618)

c)

Interpretation: We are 90% confident that the true value of the difference between the two population proportions lies between -0.19 and -0.04618.

Let Null hypothesis be that there is no difference in proportion of purebred dingoes between Queensland and South Australia. Based on the 90% confidence intervals, it can be concluded that there is a difference in the proportion of purebred dingoes between Queensland and South Australia because there is strong evidence against rejecting the null hypothesis.