Question

Consider the following competing hypotheses and accompanying sample data. (You may find it useful to reference the appropriate table: z table or t table)

H₀: p₁ − p₂ ≥ 0
H_A: p₁ − p₂ < 0

x1 = 250	x2 = 275
n1 = 400	n2 = 400

a. 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. 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

c. At the 5% significance level, what is the conclusion to the test?

• Reject H₀ since the p-value is less than significance level.

• Reject H₀ since the p-value is greater than significance level.

• Do not reject H₀ since the p-value is less than significance level.

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

d. Interpret the results at αα = 0.05.

• We conclude that the population proportions differ.

• We cannot conclude that the population proportions differ.

• We conclude that population proportion 2 is greater than population proportion 1.

• We cannot conclude that population proportion 2 is greater than population proportion 1.

rev: 01_22_2019_QC_CS-154677

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Answer 1

The estimate of the sample proportion is ,

The pooled estimate is ,

The null and alternative hypothesis is ,

a.The test statistic is ,

b. The p-value is ,

p-value= ; From standard normal distribution table

0.025 < p-value < 0.05

c.

Reject Ho , since the p-value is less than significance level 0.05

d. Conclusion : We conclude that population proportion 2 is greater than population proportion 1.