Question

the weights of four randomly and independently selected bags of potatoes labeled 20 pounds were found 21.7,22,20.5, and 21.9. Assume Normality. Using a two sided alternative hypothesis should you be able to reject a hypothesis that the population mean is 20 pounds using a significance level of 0.05 why or why not the confidence interval is reported here I am 95% confidence the population mean is between 20.4 and 22.6 pounds. B) test the hypothesis that the population mean is not 20. Use a significant level of 0.05. The test statistic and p-value are?

side note: i get stuck on finding the Standard deviation and then inserting it to get t stats. If you can please go step by step, really struggling.

Answer 1

	x	x2
	21.7	470.89
	22	484
n=	20.5	420.25
4	21.9	479.61
sum =	86.1	1854.75
mean=	21.525	463.6875
s2 =	0.4825
df= n-1 =4-1 =3
s2=	1/n-1 {(sum x2 -(sum x)2/n}

95% confidence interval is given by

21.525 1.105144

{20.42, 22.63 }

so We reject population mean is 20 pounds

now

H0 :

H1:  two sided alternative

significance level of =0.05

Test Statistics.   

  

Test Statistics t = 4.3908

p-value = 0.023

Conclusion: p-value( 0.023) <0.05

so Reject Ho that is we reject population mean is 20 pounds