Question

A random sample of 19 rainbow trout caught at Brainard lake, Colorado, had mean length x = 11.9 inches with sample standard deviation o 2.8 inches.
Find a 95% confidence interval for the population mean length of all rainbow trout in this lake.
b. interpret the meaning of the confidence interval in the context of this problem .

A random sample of 78 students was interviewed, and 59 students said that they would vote for Jennifer James as student body president.
a. Let p represent the proportion of all students at this college who will vote for Jennifer. Find a point estimate p for p.
b. Find a 98% confidence interval for p.

Answer 1

1)

a)

t critical value at 0.05 level with 18 df = 2.101

95% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

11.9 - 2.101 * 2.8 / sqrt(19) < < 11.9 + 2.101 * 2.8 / sqrt(19)

10.55 < < 13.25

95% CI is ( 10.55 , 13.25 )

b)

Interpretation - We are 95% confident that the population mean length of all rainbow trout in this lake is between

10.55 inch and 13.25 inch

2)

a)

sample proportion = 59 / 78 = 0.756

b)

98% confidence interval for p is

- Z * sqrt [ ( 1 - ) / n ] < p < + Z * sqrt [ ( 1 - ) / n ]

0.756 - 2.326 * sqrt [ 0.756 (1 - 0.756) / 78] < p < 0.756 + 2.326 * sqrt [ 0.756 (1 - 0.756) / 78]

0.643 < p < 0.869

98% CI is ( 0.643 , 0.869 )