Wild fruit flies have red eyes. A recessive mutation produces white-eyed individuals. A researcher wants to...

Wild fruit flies have red eyes. A recessive mutation produces white-eyed individuals. A researcher wants to assess the proportion of heterozygous individuals. A heterozygous red-eyed fly can be identified through its off-spring. When crossed with a white-eyed fly it will have a mixed progeny.

A random sample of 100 red-eyed fruit flies was taken. Each was crossed with a white- eyed fly. Of the sample flies, 12 were shown to be heterozygous because they produced mixed progeny.

a) Check this data for the conditions necessary for the calculation of a large-sample confidence interval. Does it comply OR should you use the plus-four interval only?

b) Calculate the summary statistics from these data.

c) Determine a 95% confidence interval for the proportion of heterozygous flies.

d) Also use a test of significance at the 5% level to test the hypothesis that the proportion of heterozygous red-eyed flies is different to a proposed theoretical value of 17%?

e) Compare the answer from this test at the 5% level in d) to the conclusion you could make from the 95% confidence interval in c). Would you necessarily expect the same answer?

Solutions

Expert Solution

a) The sample proportion is calculated as . W have . So we can calculate a large-sample confidence interval.

b)The confidence interval for proportion is

Here .

The test statistic is

c) The 95% CI for proportion is (Here )

d) The test statistic is

Since the test statistic is , the hypothesis that the proportion of heterozygous red-eyed flies is different to a proposed theoretical value of 17% is rejected.

e) Since , the confidence interval includes the proposed theoretical value of 17%. Hence, there is no diffefence in proportions. Same as part (d).

milcah answered 3 weeks ago

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