## Related questions with answers

Claim: Most adults would erase all of their personal information online if they could. A GFI Software survey of 565 randomly selected adults showed that 59% of them would erase all of their personal information online if they could. Find the value of the test statistic.

Solutions

VerifiedGiven:

$n=565$

$\hat{p}=59\%=0.59$

The percentage of 59% represents the proportion of a sample and thus we are making a claim about the population proportion $p$ in the hypotheses.

We claim "most of the adults", which indicates more than 50% or 0.50:

$p>0.50$

The null hypothesis states that the population proportion is equal to the value mentioned in the claim.

$H_0:p=0.50$

The claim is either the null hypothesis or the alternative hypothesis. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

$H_a:p>0.50$

Determine the value of the test-statistic:

$z=\dfrac{\hat{p}-p_0}{\sqrt{\dfrac{p_0(1-p_0)}{n}}}=\dfrac{0.59-0.50}{\sqrt{\dfrac{0.50(1-0.50)}{565}}}\approx 4.28$

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