Question

A survey of 1060 randomly selected US teens ages 13 to 17 found that 605 of them say they have made a new friend online.

Find and interpret a 90% confidence interval for the proportion of US teens who have made a new friend online.

Fill in the blanks

a) The scenario above represents (write either test or CI):

b) The population parameter (write either single proportion or single mean):

c) The sample size:

d) The sample statistic (round decimal answer to 2 decimal places):

e) Look at the table below and state the value of z* for 90% confidence level:

Answer 1

A survey of N = 1060 randomly selected US teens ages 13 to 17 found that X = 605 of them say they have made a new friend online.

The confidence interval is calculated as:

Where the sample proportion is calculated as:

and the Zc at 90% confidence level is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.95), thus the Zc is computed as 1.645.

Now the confidence interval is calculated as:

Interpretation:

Thus at 90 % confidence, we can say that the confidence interval for the true population proportion is between 0.546 and 0.596.

Fill in the blanks

a) The scenario above represents (write either test or CI):

This represents the confidence interval CI

b) The population parameter (write either single proportion or single mean):

The population parameter is the value with help of which we can estimate the population, here the population parameter is sample proportion.

c) The sample size:

The sample is the no of value on which the experiments are conducted and taken from a large population, here the sample size is N = 1060

d) The sample statistic (round decimal answer to 2 decimal places):

The sample statistic is the sample proportion which is calculated as:

Thus 0.57

e) Look at the table below and state the value of z* for a 90% confidence level:

The Z value is at 90% confidence level is calculated using the excel formula for normal distribution which is =NORM.S.INV(0.95), thus the Zc is computed as 1.645.