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Use the method specified to perform the hypothesis test for the population mean µ. The highest acceptable level of pesticide found in quail has been limited to 0.35 parts per million (ppm). A hunting organization measured the level of the pesticide found in quail harvested from field trails. The group gathered data from a random sample of 20 quail. The sample produced a sample proportion of .44. Assume that the population standard deviation of σ = 0.21 ppm. At a = 0.05, does the data provide sufficient evidence to conclude that the mean level of pesticide is greater that the limit of 0.35 ppm.
a. Use the critical value z0 method from the normal distribution.
1. H0 : µ = .35
Ha : µ ≠ .35
2.a = 0.05 (one tail)
3.Test statistics: (0.44-0.35)/ (0.21/√20) = 1.92
4.P-value or critical z0 or t0.: z0 = 1.96
5. Rejection Region: Z<-1.96 or Z>1.96
6. Decision: do not reject Ho
7. Interpretation: not sufficient evidence to conclude that the mean level of pesticide is greater that the limit of 0.35 ppm.
b. Use the P-value method.
4.P-value or critical z0 or t0.
a. If you are using a one-tailed test, then:
Ha: μ > .35
You would reject, if Z ≥ 1.645 for P ≤ .05.
In your conclusion, you need to state that the value is or is not "significantly greater."
I did not check your calculations.