Question

In a study of environmental effects upon reproduction, 123 female adult white-tailed deer from the central Adirondack area were captured, and 97 were found to be pregnant. Construct a 99% Wilson Adjusted confidence interval for the proportion of females pregnant in this deer population.

For all hypothesis tests, you must show the four steps:

1. Hypotheses

2. Test statistic

3. p-value or p-value approximation

4. Conclusion sentence (Do no just say ”Reject the null hypothesis” or ”Fail to reject the null hypothesis”)

Answer 1

Solution :

n = 123

x = 97

Point estimate = sample proportion = = x / n = 97/123 = 0.789

1 - = 1 -0.789 = 0.211

Z/2 = 2.576

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 2.576 * ((0.789*(0.211) /123 )

= 0.095

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.789-0.0 95 < p < 0.789 +0.095

0.694 < p < 0.883

( 0.694,0.883 )

1)

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.50

Ha : p 0.50

= x / n = 97/123 = 0.789

P0 = 0.50

1 - P0 = 0.50

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.789- 0.50/ [0.50*(0.50) /123 ]

= 6.41

P(z > 6.41) = 1 - P(z <6.41 ) = 0

P-value = 0.0000

= 0.05

0 < 0.05

Reject the null hypothesis .