Question

n 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 ≥ 0.35; HA: p < 0.35.

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 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10

a-3. At the 0.05 significance level, What is the conclusion? Reject H0 since the p-value is greater than significance level. Reject H0 since the p-value is smaller than significance level. Do not reject H0 since the p-value is greater than significance level. Do not reject H0 since the p-value is smaller than significance level.

a-4. Interpret the results at α = 0.05 We conclude that the population mean is less than 0.35. We cannot conclude that the population mean is less than 0.35. We conclude that the population proportion is less than 0.35. We cannot conclude that the population proportion is less than 0.35. H0: p = 0.35; HA: p ≠ 0.35.

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 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10

b-3. At the 0.05 significance level, What is the conclusion? Reject H0 since the p-value is greater than significance level. Reject H0 since the p-value is smaller than significance level. Do not reject H0 since the p-value is greater than significance level. Do not reject H0 since the p-value is smaller than significance level.

b-4. Interpret the results at α = 0.05. We conclude that the population mean differs from 0.35. We cannot conclude that the population mean differs from 0.35. We conclude the population proportion differs from 0.35. We cannot conclude that the population proportion differs from 0.35.

Answer 1

a-1)
pcap = 87/290 = 0.3

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n))
z = (0.3 - 0.35)/sqrt(0.35 * 0.65/290)
z = -1.79

a-2)
p-value < 0.05

a-3)
Reject H0 since the p-value is smaller than significance level

a-4)
We conclude that the population proportion is less than 0.35.

b-1)
pcap = 87/290 = 0.3

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n))
z = (0.3 - 0.35)/sqrt(0.35 * 0.65/290)
z = -1.79

b-2)
0.05 < p-value < 0.10

b-3)
Do not reject H0 since the p-value is greater than significance level

b-4)
We cannot conclude that the population proportion differs from 0.35.