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.
Answer:
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.
Answer:
1.H0 :
Ha :
2.a =
3.Test statistics:
4.P-value or critical z0 or t0.
5.Rejection Region:
6.Decision:
7.Interpretation:
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.
To perform the hypothesis test for the population mean µ using the P-value method, follow these steps:
1. Formulate the null and alternative hypotheses:
- H0: µ = 0.35 (Mean level of pesticide is equal to the limit of 0.35 ppm)
- Ha: µ > 0.35 (Mean level of pesticide is greater than the limit of 0.35 ppm)
2. Set the significance level (alpha), in this case, a = 0.05 (one tail).
3. Calculate the test statistic:
- Test Statistic = (Sample Mean - Population Mean) / (Population Standard Deviation / √ Sample Size)
- Test Statistic = (0.44 - 0.35) / (0.21 / √20)
- Test Statistic = 1.92
4. Find the P-value or critical value:
- The P-value is the probability of obtaining a test statistic as extreme as the one observed or more extreme assuming the null hypothesis is true.
- To find the P-value, we need to use a standard normal distribution table or a statistical software.
- From the information given, we know the P-value = ???
5. Rejection Region:
- To determine the rejection region, we compare the P-value to the significance level (alpha).
- If P-value < alpha, we reject the null hypothesis.
- If P-value ≥ alpha, we fail to reject the null hypothesis.
6. Make a decision:
- If the P-value < alpha, reject the null hypothesis.
- If the P-value ≥ alpha, fail to reject the null hypothesis.
7. Interpretation:
- If we reject the null hypothesis, there is sufficient evidence to conclude that the mean level of pesticide is greater than the limit of 0.35 ppm.
- If we fail to reject the null hypothesis, there is not enough evidence to conclude that the mean level of pesticide is greater than the limit of 0.35 ppm.
Note: Without the actual P-value or critical values, we cannot give a specific decision or interpretation for this particular test using the P-value method.