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In: Statistics and Probability

n order to conduct a hypothesis test for the population proportion, you sample 450 observations that...

n order to conduct a hypothesis test for the population proportion, you sample 450 observations that result in 207 successes. (You may find it useful to reference the appropriate table: z table or t table)

H0: p ≥ 0.52; HA: p < 0.52.

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.

  • 0.05 p-value < 0.10
  • p-value 0.10
  • p-value < 0.01

  • 0.01 p-value < 0.025
  • 0.025 p-value < 0.05

a-3. At the 0.01 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 αα = 0.01

  • We conclude that the population mean is less than 0.52.

  • We cannot conclude that the population mean is less than 0.52.

  • We conclude that the population proportion is less than 0.52.

  • We cannot conclude that the population proportion is less than 0.52.

H0: p = 0.52; HA: p ≠ 0.52.

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.

  • 0.05 p-value < 0.10
  • p-value 0.10
  • p-value < 0.01

  • 0.01 p-value < 0.025
  • 0.025 p-value < 0.05

b-3. At the 0.01 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 αα = 0.01.

  • We conclude that the population mean differs from 0.52.

  • We cannot conclude that the population mean differs from 0.52.

  • We conclude the population proportion differs from 0.52.

  • We cannot conclude that the population proportion differs from 0.52.

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