Question

In order to conduct a hypothesis test for the population proportion, you sample 450 observations that result in 189 successes. (You may find it useful to reference the appropriate table: z table or t table) H0: p ≥ 0.45; HA: p < 0.45. 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. 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 0.01 p-value < 0.025 a-3. At the 0.10 significance level, What is the conclusion? Do not reject H0 since the p-value is smaller than significance level. Do not reject H0 since the p-value is greater than significance level. Reject H0 since the p-value is smaller than significance level. Reject H0 since the p-value is greater than significance level. a-4. Interpret the results at α = 0.10 We cannot conclude that the population mean is less than 0.45. We conclude that the population mean is less than 0.45. We cannot conclude that the population proportion is less than 0.45. We conclude that the population proportion is less than 0.45. H0: p = 0.45; HA: p ≠ 0.45. 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. 0.01 p-value < 0.025 0.025 p-value < 0.05 0.05 p-value < 0.10 p-value 0.10 p-value < 0.01 b-3. At the 0.10 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 = 0.10. We conclude that the population mean differs from 0.45. We cannot conclude that the population mean differs from 0.45. We conclude the population proportion differs from 0.45. We cannot conclude that the population proportion differs from 0.45.

Answer 1

a1)

test statistics:

pcap = 189/450 = 0.42

z = (pcap -p)/sqrt(p*((1-p)/n)
= (0.42 - 0.45)/sqrt(0.45*(1-0.45)/450)
= -1.2792

a2)

p value = 0.1004

pvalue > 0.10

a3)

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

a4)

at α = 0.10 We cannot conclude that the population proportion is less than 0.45.

b1)

test statistics:

pcap = 189/450 = 0.42

z = (pcap -p)/sqrt(p*((1-p)/n)
= (0.42 - 0.45)/sqrt(0.45*(1-0.45)/450)
= -1.2792

b2)

pvalue = 0.2008

pvalue > 0.10

b3)
Do not reject H0 since the p-value is greater than significance level

b4)
. We cannot conclude that the population proportion differs from 0.45.