Mathematics: The government of preon (a small island nation) was voted in at the last election with 68% of the votes. that was 2 years ago, and ever since then the government has assumed that their approval rating has been the same. some recent events have affected public opinion and the government suspects that their approval rating might have changed. they decide to run a hypothesis test for the proportion of people who would still vote for them.the null and alternative hypotheses are: h0: pi symbol = 0.68ha:

I think it is B but if I’m wrong I’m very sorry...

The government of preon (a small island nation) was

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natalie2sheffield

11.01.2022

Mathematics

1.41

Step-by-step explanation:

Test statistic(z) for proportion is given by :-

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}$

, where p=population proportion.

$\hat{p}$ = sample proportion

n= sample size.

As per given , we have

$H_0:\mu=0.68\\\\ H_a: \mu\neq0.68$

n= 102

$\hat{p}=0.745$

Then, the test statistic (z) for this hypothesis test will be :-

$z=\dfrac{0.745-0.68}{\sqrt{\dfrac{0.68(1-0.68)}{102}}}\\\\=\dfrac{0.065}{\sqrt{\dfrac{0.2176}{102}}}\\\\=\dfrac{0.065}{\sqrt{0.0021333}}\\\\=\dfrac{0.065}{0.04618802}=1.40729132792\approx1.41$

[Rounded to the two decimal places]

Hence, the test statistic (z) for this hypothesis test = 1.41

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