Question

​Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 564 randomly selected adults showed that 56​% of them would erase all of their personal information online if they could. Find the value of the test statistic.

Answer 1

The value of z test statistic is 2.871.

Explanation:

We are given that a software firm survey of 564 randomly selected adults showed that 56​% of them would erase all of their personal information online if they could. Find the value of the test statistic.

Let p = population proportion of adults who would erase all of their personal information online if they could.

So, Null Hypothesis,
`H_0` : p
`\leq` 50% {means that adults who would erase all of their personal information online if they could is less than or equal to 50%}

Alternate Hypothesis,
`H_A` : p > 50% {means that majority of adults would erase all of their personal information online if they could}

The test statistics that would be used here One-sample z test for proportions;

T.S. =
`\frac{\hat p-p}{\sqrt(\hat p(1-\hat p))/(n) {} }` ~ N(0,1)

where,
`\hat p` = sample proportion of adults who would erase all of their personal information online if they could = 56%

n = sample of adults taken = 564

So, the test statistics =
`\frac{0.56-0.50}{\sqrt(0.56(1-0.56))/(564) {} }`

= 2.871

The value of z test statistic is 2.871.