Question

1. Determine whether to use z_{α /2} or  t_{α /2} . Find the critical value.

Given n = 8 and s = 3 for a 95% confidence interval.

2. Find t_{α /2} with  n = 24 for a 98% confidence interval.

3. In a study of 100 middle school children, the mean number of hours weekly spent playing video games was 15 hours with a standard deviation of 2 hours. Find the point estimate for the true mean number of hours weekly that middle school children spent playing video games.

4.

A survey of 40 parents found that 80% were worried about their kids spending too much time texting. Find the point estimate p-hat for the population proportion. Also, find the value of q-hat.

Type your answer in a form :

p-hat= ,  q-hat =

Answer 1

Solution :

Given that,

1) sample standard deviation = s = 3

sample size = n = 8

Degrees of freedom = df = n - 1 = 8 - 1 = 7

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,7 = 2.365

2) sample size = n = 24

Degrees of freedom = df = n - 1 = 24 - 1 = 23

At 98% confidence level

= 1 - 98%

=1 - 0.98 =0.02

/2 = 0.01

t/2,df = t0.01,23 = 2.500

3) mean = = 15

standard deviation = = 2

n = 100

Point estimate = = 15

4) Point estimate = sample proportion = = 0.80

q^ = 1 - = 1 - 0.80 = 0.20