Question 977800
a)

This is a right tailed test. So we want to find the value k that makes P(Z > k) = 0.05 true.

Use a table like <a href="http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf">this one</a>. Look at the bottom Z row. Then find the column that has "0.05" in the "one tail row". The intersection of the row and column leads to 1.645


So 1.645 is the critical value we're after. That rounds to 1.65


Decision Rule: Reject H0 if z > <font color="red">1.65</font>


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b)

Standard Error:
{{{SE = sqrt((pi*(1-pi))/n)}}}
{{{SE = sqrt((0.83*(1-0.83))/140)}}}
{{{SE = 0.03174676586452}}} (approximate)


Test Statistic
{{{z = (p - pi)/(SE)}}}
{{{z = (0.88-0.83)/(0.03174676586452)}}}
{{{z = 1.57496357938871}}}
{{{z = 1.57}}}


The test statistic is <font color="red">1.57</font>

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c)


Go back to part a) where the decision rule is set up.


The critical value is 1.65 and the test statistic 1.57


Since the test statistic is NOT larger than the critical value, we <font color="red"><u>fail</u> to reject</font> the null hypothesis.


We do not have enough evidence to reject the null.