Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.
  Ho:μ=50.8Ho:μ=50.8
      Ha:μ≠50.8Ha:μ≠50.8
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=26n=26 with mean M=62.7M=62.7 and a standard deviation of SD=18.4SD=18.4.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 50.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 50.8.
• The sample data support the claim that the population mean is not equal to 50.8.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 50.8.

You wish to test the following claim (HaHa) at a significance level of α=0.002α=0.002.

      Ho:μ=52.4Ho:μ=52.4
      Ha:μ≠52.4Ha:μ≠52.4
You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=112n=112 with mean M=48.9M=48.9 and a standard deviation of SD=15.3SD=15.3.
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =
What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =
The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.4.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 52.4.
• The sample data support the claim that the population mean is not equal to 52.4.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 52.4.

Answer 1

Q1)  Ho:μ=50.8
Ha:μ≠50.8

Level of Significance (l.o.s.) : α = 0.001.

Decision Criteria : Reject Ho at 0.1% l.o.s. if p-value <  α

Calculation : = 62.7, n = 26 & s = 18.4

T

t cal =  $\frac{\bar{x}-\mu}{s/\sqrt{n}}$  =  $\frac{62.7-50.8}{18.4/\sqrt{26}}$ = 3.2977 = 3.298

p-value = P( | t | < 3.298 ) = 0.0015

Conclusion : Since p-value is greater than α, we fail to reject Ho at 1% l.o.s. &
As such, the final conclusion is that there is not sufficient sample evidence to support the claim that the population mean is not equal to 50.8.

Q1)  Ho:μ=52.4
Ha:μ≠52.4

Level of Significance (l.o.s.) : α = 0.002.

Decision Criteria : Reject Ho at 0.2% l.o.s. if p-value < α

Calculation : = 48.9, n = 112 & s = 15.3

T

t cal =  $\frac{\bar{x}-\mu}{s/\sqrt{n}}$  =  $\frac{48.9-52.4}{15.3/\sqrt{112}}$ = -2.42095 = -2.421

p-value = P( | t | < -2.421) = 0.0086

Conclusion : Since p-value is greater than α, we fail to reject Ho at 0.2% l.o.s. &
As such, the final conclusion is that there is not sufficient sample evidence to support the claim that the population mean is not equal to 52.4.

Hope this answers your query!