Question

Claim: Most adults would erase all of their personal information online if they could.

A software firm survey of 453 randomly selected adults showed that 60% of them would erase all of their personal information online if they could.
a. Find the value of the test statistic. (Round to two decimal places as needed.)

Answer 1

t = 4.26

Explanation:

Sample, n = 453

Proportion, x = 60%

Required

Test Statistic

Test statistic is calculated as follows

t = (x - p)/(σ/√n)

Where σ = √p(1 - p)

When an experiment is conducted repeatedly, the results moves close to the expected value (Law of large numbers).

Hence p = 0.5

Calculating σ

σ = √p(1 - p)

σ = √0.5(1 - 0.5)

σ = √(0.5 * 0.5)

σ = √0.5²

σ = 0.5

So,

t = (x - p)/(σ/√n) becomes

t = (60% - 0.5)/(0.5/√453)

t = (0.6 - 0.5)/(0.5/√453)

t = (0.1)/(0.5/21.28)

t = 0.1 * 21.28/0.5

t = 2.128/0.5

t = 4.256

t = 4.26 ---- Approximated