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A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If the researcher obtains a sample mean of M = 88, which combination of factors is most likely to result in rejecting the null hypothesis? Group of answer choices ​σ = 10 and α = .05 ​σ = 5 and α = .01 ​σ = 5 and α = .05 ​σ = 10 and α = .01

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Answer:

If ​σ = 5 and α = .05 then we can reject the null hypothesis.

Explanation:

z-score of the sample mean is calculated using the formula:

z=[tex]\frac{X-M}{s}[/tex] where

  • X is the sample mean
  • M is the population mean
  • s=σ  is the standard deviation

If the p value of the z score is smaller than the significance level (α)  then null hypothesis will be rejected.

If s= ​σ = 10 and α = .05 then

z=[tex]\frac{88-80}{10}[/tex] =0.8 and corresponding p value ≈ 0.21

The result is not significant at p ≤ 0.05 therefore we fail to reject the null hypothesis.

If ​σ = 5 and α = .01 then

z=[tex]\frac{88-80}{5}[/tex] =1.6 and corresponding p value ≈0.05

The result is not significant at p ≤ 0.01 therefore we fail to reject the null hypothesis.

If ​σ = 5 and α = .05 then

z=[tex]\frac{88-80}{5}[/tex] =1.6 and corresponding p value≈0.05

The result is significant at p ≤ 0.05 therefore we can reject the null hypothesis.

If ​σ = 10 and α = .01 then

z=[tex]\frac{88-80}{10}[/tex] =0.8 and corresponding p value = 0.21

The result is not significant at p ≤ 0.01 therefore we fail to reject the null hypothesis.