Question

From your sample of 80​ 5-year-old girls, you notice that 9 of them have​ red-hair.

Find and interpert a​ 99% confidence interval for the proportion of​ red-haired 5-year-olds.

1. State the confidence interval​ (round to 4 decimal​ places):

2. Interpert the confidence interval in the SHOW YOUR WORK area.

3. You were told that​ 2% of the population is​ red-haired. Based on your​ interval, you can conclude​ that:

A.

the proportion you were told is correct since​ 2% is within the interval.

B.

the proportion of​ red-hair 5-year-olds is higher than​ 2% since​ 2% is higher than the sample proportion.

C.

the proprotion of​ red-hair 5-year-olds is lower than​ 2% since​ 2% is higher than the interval.

D.

the proportion of​ red-hair 5-year-olds is higher than​ 2% since​ 2% is lower than the interval.

Answer 1

1). The Confidence interval is calculated as

Where,

Which is the sample proportion and n=80 is the sample size

Z is calculated using Z table shown below at 99 % confidence level which is 2.58 here.

so now

={0.0214, 0.2036}

2. Interpretation :

We can be 99 % confident that the true proportion of read haired 5 year old are in between {0.0214, 0.2036}

3. The proportion we were told is incorrect because 2 % is not in the interval.

The options seems to be ambigious but still i go with.