Question

Our environment is very sensitive to the amount of ozone in the upper atmosphere. The level of ozone normally found is 5.1 parts/million (ppm). A researcher believes that the current ozone level is not at the normal level. The mean of 8 samples is 5.3 ppm with variance of 0.64. Does the data support the claim at the 0.1 level? Assume the population distribution is approximately normal. Use either the p-value or the critical value approach to arrive at your conclusion. Show supporting work by including and clearly labeling each of the 4 steps used to arrive at your solution. Be sure to write a full conclusion, complete sentence and alternative hypotheses.

Step 2: Find the P-value for the hypothesis test. Round your answer to four decimals.

Step 3: Make the decision to reject or fail to reject the null hypotheses

Answer 1

step 2:

null hypothesis: HO: μ		=	5.1
Alternate Hypothesis: Ha: μ		≠	5.1
0.1 level with two tail test and n-1= 7 df, critical t=				1.895
Decision rule :reject Ho if absolute value of test statistic|t|>1.895
	population mean μ=	5.1
	sample mean 'x̄=	5.300
	sample size   n=	8.00
	sample std deviation s=	0.800
	std error 'sx=s/√n=	0.283
	test stat t ='(x-μ)*√n/sx=	0.707
	p value      =	0.5024

step 3:

since p value >0.1 ;  fail to reject the null hypotheses

we do not have have sufficient evidence to conclude that  the current ozone level is not at the normal level.