In order to conduct a hypothesis test for the population proportion, you sample 400 observations that result in 212 successes. (You may find it useful to reference the appropriate table: z table or t table)
H_{0}: p ≥ 0.54; H_{A}: p < 0.54.
a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
a-2. Find the p-value.
p-value < 0.01
a-3. At the 0.01 significance level, What is the conclusion?
Do not reject H_{0} since the p-value is smaller than significance level.
Do not reject H_{0} since the p-value is greater than significance level.
Reject H_{0} since the p-value is smaller than significance level.
Reject H_{0} since the p-value is greater than significance level.
a-4. Interpret the results at αα = 0.01
We cannot conclude that the population mean is less than 0.54.
We conclude that the population mean is less than 0.54.
We cannot conclude that the population proportion is less than 0.54.
We conclude that the population proportion is less than 0.54.
H_{0}: p = 0.54; H_{A}: p ≠ 0.54.
b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
b-2. Find the p-value.
p-value < 0.01
b-3. At the 0.01 significance level, What is the conclusion?
Reject H_{0} since the p-value is greater than significance level.
Reject H_{0} since the p-value is smaller than significance level.
Do not reject H_{0} since the p-value is greater than significance level.
Do not reject H_{0} since the p-value is smaller than significance level.
b-4. Interpret the results at αα = 0.01.
We conclude that the population mean differs from 0.54.
We cannot conclude that the population mean differs from 0.54.
We conclude the population proportion differs from 0.54.
We cannot conclude that the population proportion differs from 0.54.
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