Question

In order to conduct a hypothesis test for the population mean, a random sample of 28...

In order to conduct a hypothesis test for the population mean, a random sample of 28 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 17.9 and 1.5, respectively. (You may find it useful to reference the appropriate table: z table or t table).

H0: μ ≤ 17.5 against HA: μ > 17.5


a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

a-2. Find the p-value.

  • p-value < 0.01

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

  

a-3. At the 1% significance level, what is the conclusion?

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

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

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

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



a-4. Interpret the results at αα = 0.01.

  • We cannot conclude that the population mean is greater than 17.5.

  • We conclude that the population mean is greater than 17.5.

  • We cannot conclude that the population mean differs from 17.5.

  • We conclude that the population mean differs from 17.5..

H0: μ = 17.5 against HA: μ ≠ 17.5

b-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

b-2. Find the p-value.

  • p-value 0.10
  • 0.01 p-value < 0.025
  • p-value < 0.01

  • 0.05 p-value < 0.10
  • 0.025 p-value < 0.05

b-3. At the 1% significance level, what is the conclusion?

  • 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.



b-4. Interpret the results at αα = 0.01.

  • We conclude that the population mean is greater than 17.5.

  • We cannot conclude that the population mean is greater than 17.5.

  • We conclude that the population mean differs from 17.5.

  • We cannot conclude that the population mean differs from 17.5.

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