Answer the following questions in the space provided below:
1.For a logging tract to be economically viable at least 80% of the trees in the tract must be economically valuable species. You have been hired to evaluate a large tract for a logging company. In a random sample of 75 trees, you find that 58 of them are of an economically viable species. Your client is only willing to accept a risk of 5% for purchasing the logging rights to the tract if it is not economically viable. Use statistical testing to determine if you should recommend that the tract be purchased or not.
a)State the Null and Alternative Hypotheses you will use for your test.
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State your test statistic, and define its sampling distribution
d)Calculate the value of your test statistic
e)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
2.The Canadian drinking water guideline for arsenic sets a Maximum Acceptable Concentration of 0.010 mg/L. A random sample of n=30 households in a city yields an average arsenic concentration of 0.014 mg/L, with a standard deviation of 0.01 mg/L. Test the assertion that the arsenic concentration is actually above the regulated limit using a 1% significance level. (3 marks total)
a)State the Null and Alternative Hypotheses you will use for your test
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State your test statistic, and define its sampling distribution
d)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
3.Calculate the 99% quantile of the F distribution with df1=10 and df2=12.
4.Calculate for an F-distribution with df1=6 and df2=4.
5.Calculate for an F-distribution with df1=10 and df2=5.
6.The sample standard deviation of the mercury concentration in whole blood (mEq/L) for n1=20 trout from brownwater lake was found to be s1=40.5, while the sample standard deviation of concentration for n2=20 trout from stony lake was s2=32.1. Assuming normality of the two concentration distributions, test at a 10% significance level to see if the data suggests any differences between concentration variances for the fish in the two lakes.
a)State the Null and Alternative Hypotheses you will use for your test
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic, and define its sampling distribution
d)Calculate the value of your test statistic
e)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
7.Is someone who switches product brands due to sale pricing is less likely to remain brand loyal than someone who switches for other reasons? To address this question, you collect data on people who purchased Red Pig Road beer due to a sale event. Your data reveals that 30 out of 200 people who bought Red Pig Road beer due to sale pricing remained brand loyal after the sale pricing ended, whereas 180 out of 600 people tried Red Pig Road beer for other reasons continued to purchase Red Pig Road beer after the sale pricing ended. Test your hypotheses at a 5% significance level.
a)State the Null and Alternative Hypotheses you will use for your test.
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic and define its sampling distribution.
d)Calculate the value of the test statistic.
e)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
8.A sample of 300 urban adult residents of a particular province revealed 63 who favoured increasing the highway speed limit from 110 to 120 kph, while a sample of 180 rural residents yielded 75 who favoured the increase. Does this data indicate that the sentiment for increasing the speed limit is different for the two groups of residents? Test your hypotheses at the 5% level.
a)State the Null and Alternative Hypotheses you will use for your test
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic, and define its sampling distribution
d)Calculate the value of the test statistic
e)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
9.Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. A study on the effect of toxaphene on animals has revealed that animals exposed to a low dose of toxaphene exhibit weight gain, whereas animals not exposed to toxaphene do not. The sample standard deviation of weight gain for 23 animals not exposed to toxaphene was 32 g, whereas the sample standard deviation of weight gain for 20 animals exposed to toxaphene was 54 g. Do these data suggest that there is more variability in weight gains for animals exposed to toxaphene? Assume normality of the weight gain data, and perform your test at a 5% significance level.
a)State the Null and Alternative Hypotheses you will use for your test
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic, and define its sampling distribution.
d)Calculate the value of your test statistic.
e)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
10.You have been hired to determine whether residential water usage is higher in Kamloops than it is in Kelowna. From a sample of n=100 measurements, you have determined the mean water use in Kamloops to be 350 liters per day with a standard deviation of 56. From a sample of n=200 measurements, you have determined the mean water use in Kelowna to be 300 liters per day, with a standard deviation of 45. Using these sample statistics, perform a statistical test to answer the question of whether residential water usage is higher in Kamloops than it is in Kelowna. Use a significance level of 5%, and assume the data are approximately normal.
a)State the Null and Alternative hypotheses you will use to test your research question.
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic and define its sampling distribution.
d)Calculate the test statistic.
e)Estimate the PROB-VALUE for your test, and state whether or not you can reject the null hypothesis.
11.It is hypothesized that the presence of carpet may increase the number of airborne bacteria in a room. To test this hypothesis, the airborne bacteria count was measured in a sample of 8 carpeted and 8 uncarpeted hospital rooms. The data for the carpeted rooms are shown below. Assuming normality of these data perform a test at a 5% significance level to evaluate the hypothesis.
Carpeted11.88.27.113.010.810.114.614.0
Uncarpeted12.18.33.87.212.011.110.113.7
a)State the Null and Alternative hypotheses you will use to test your research question.
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic and define its sampling distribution.
d)Calculate the test statistic.
e)Estimate the PROB-VALUE for your test, and state whether you can reject the null hypothesis.
12.You would like to know if the application of fertilizer has an impact on the canopy density (i.e. leaf area) of a species of pine tree (Pinus elliotti). To do this you randomly assign a group of 8 trees to receive fertilizer application and monitor 8 additional trees that do not receive fertilization. The resulting data are shown below. Test the assertion that fertilizer increases the mean tree density at a 5% significance level. Assume that the data from the two samples are normally distributed.
Fertilized 10241216 1312 1280 1216 1312 992 1120
Unfertilized 1104 1072 1088 1328 1376 1280 1120 1200
a)State the Null and Alternative hypotheses you will use to test your research question.
b)State what type (i.e., lower tail, upper tail, or two tailed) of test you will perform
c)State the test statistic, and define its sampling distribution
e)Calculate the test statistic. Estimate the PROB-VALUE for your test, and state whether you can reject the null hypothesis.
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