Question

In a Pew Research Center poll of 745 randomly selected adults, 589 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 75% of adults say that it is morally wrong to not report all income on tax returns.a. What is the null and alternative hypothesis?b. What is the test statistic?c. What is the P-value?d. What is the Conclusion?

Answer 1

a

The null hypothesis is
`H_o : p = 0.75`

The alternative hypothesis is
`H_a : p \\e 0.75`

b

`t = 2.51`

c

`p-value = 0.01207`

d

There no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns

Explanation:

From the question we are told that

The sample size is
`n = 745`

The number that said it is morally wrong is
`k = 589`

The level of significance is
`\alpha = 0.01`

The population proportion is
`p = 0.75`

Generally the sample proportion is mathematically represented as

`\r p = (k)/(n)`

=>
`\r p = (589)/(745)`

=>
`\r p = 0.79`

The null hypothesis is
`H_o : p = 0.75`

The alternative hypothesis is
`H_a : p \\e 0.75`

The standard error is mathematically represented as

`SE = \sqrt{(p(1-p))/(n) }`

=>
`SE = \sqrt{(0.75(1-0.75))/(745) }`

=>
`SE =0.0159`

Generally the test statistics is mathematically represented as

`t = (\r p - p )/(SE)`

=>
`t = (0.79 - 0.75 )/(0.0159)`

=>
`t = 2.51`

Generally the p-value is mathematically represented as

`p-value = 2 * P(Z > 2.51)`

From the the z-table

`P(Z > 2.51) = 0.0060366`

=>
`p-value = 2 * 0.0060366`

=>
`p-value = 0.01207`

From the calculation
`p-value >\alpha`

Hence we fail to reject the null hypothesis

Thus there no sufficient evidence to conclude that 75% of adults say that it is morally wrong to not report all income on tax returns