Question 1163236: In order to conduct a hypothesis test for the population proportion, you sample 290 observations that result in 87 successes. (You may find it useful to reference the appropriate table: z table or t table)
H0: p ≥ 0.36; HA: p < 0.36.
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.)
2. Find the p-value.
A. p-value > or equal to 0.10
B. p-value < 0.01
C. 0.01 < or equal to p-value < 0.025
D. 0.025 < or equal to p-value < 0.05
E. 0.05 < or equal to p-value < 0.10
3. At the 0.01 significance level, What is the conclusion?
A. Do not reject H0 since the p-value is smaller than significance level.
B. Do not reject H0 since the p-value is greater than significance level.
C. Reject H0 since the p-value is smaller than significance level.
D. Reject H0 since the p-value is greater than significance level.
4. Interpret the results at α = 0.01
A. We cannot conclude that the population mean is less than 0.36.
B. We conclude that the population mean is less than 0.36.
C. We cannot conclude that the population proportion is less than 0.36.
D. We conclude that the population proportion is less than 0.36.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! z=(p hat-p)/sqrt((0.36*0.64)/290)
=-0.06/0.0282=-2.13
p-value is 0.0166
Answer to 2 is C
Answer to 3 is B
Answer to 4 is C. This is a population proportion, not a mean, and at the 0.01 level, we fail to reject the null hypothesis, so there is insufficient evidence to conclude that the population proportion is < 0.36.
The p-value has to be less than the significance level, since the p-value says what the probability would be of finding a result this extreme or more, and that probability has to be lower than the postulated significance.
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