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Statistical Hypothesis Testing and Inference: A Comprehensive Assignment

This assignment covers statistical hypothesis testing and inference, guiding students through methods for testing hypotheses in various research contexts.

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    Statistical Hypothesis Testing and Inference: A Comprehensive Assignment 1. (1 pt) An agricultural field trial compares the yield of two varieties of corn. The researchers divide in half each of 19 fields of land in different locations and plant each corn variety in one half of each plot. After harvest, the yields are compared in bushels per acre at each location. The 19 differences (Variety A - Variety B) give ¯ x = 2:27 and s = 4:49. Does this sample provide evidence that Variety A had a higher yield than Variety B? (a) State the null and alternative hypotheses: (Type ”mu” for the symbol μ , e.g. mu > 1 for the mean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to 1)( Hint: Use the only equal sign in the null hypothesis) Ho: mu 1 - mu 2 =0 : Ha: mu 1 - mu 2 >0 : (b) Find the value of the test statistic. Use two decimal places. n=19, test stat : t= 2.27/4.49/sqrt(19) = 2.20 p - vlue=.0204 df=18 (c) Answer the question: Does this sample provide evidence that Variety A had a higher yield than Variety B? (Use a 5% level of significance) (Type: Yes or No ) Yes Answer(s) submitted: 2. (1 pt) Credit scores are used by banks, financial institutions, and retailers to determine one’s trustworthiness, and their ability to pay their credit card, when he/she is given a credit card. The higher the credit score, the better the credit (and the more financially trustworthy) a consumer is. In light of the current economic downturn, an economist claims that the credit score of Canadians between the ages of 25 to 40 has dropped. Prior to the current economic downturn, the mean credit score for Canadians between the ages of 25 to 40 was 673. A random sample of n = 20 Canadians between the ages of 25 to 40 was taken, the credit score of each was determined using the a certain credit bureau. The raw data is given below. 656;715;615;670;553;683;678;610;644;719;673;651;584;669;652;658;651;591;676;667 (a) Choose the correct statistical hypotheses. A. H0 : μ = 673; HA : μ 6= 673 B. H0 : X > 673; HA : X < 673 C. H0 : X = 673; HA : X < 673 D. H0 : μ > 673; HA : μ < 673 E. H0 : X = 673; HA : X 6= 673 F. H0 : μ = 673 HA : μ < 673 (b) Determine the value of the test statistic for this test, use two decimals in your answer. Test Statistic = t = (650.75 - 673)/(41.87/sqrt(20)) = - 2.38 (c) Determine the P - value for this test, to three decimal places. p - value = .014 (d) Based on the above calculations, we should reject the null hypothesis. Use alpha = 0.05

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    Answer(s) submitted: 3. (1 pt) Is the number of American - born hockey players playing in the NHL on the rise? In the 2010 - 2011 season, 24born in the United States. A random sample of n = 110 NHL hockey players found that 28 were born in the United States.Does this sample suggest that the percentage of NHL hockey players that are American - born is increasing? (a) Choose the correct statistical hypotheses. A. H0 : p > 0:24; HA : p 0:24 B. H0 : p = 0:24; HA : p 6= 0:24 C. H0 : bp < 0:24; HA : bp 0:24 D. H0 : p = 0.24 HA : p > 0. 24 E. H0 : bp = 0:24; HA : bp > 0:24 1 (b) Determine the value of the test statistic for this test, to two decimal places. Test Statistic = z= (.2545 - .24)/ sqrt(.24*.76/110)=0.36 (c) Determine the P - value for this test. Use three decimal plac es. p - value = .359 (d) Based on the above calculations, we should not reject the null hypothesis. Use alpha = 0.05 Answer(s) submitted: 4. (1 pt) According to data from the Tobacco Institute Testing Laboratory, a certain brand of cigarette contains an average of 1.4 milligrams of nicotine. An advocacy group questions this figure, and commissions an independent test to see if the the mean nicotine content is higher than the industry laboratory claims. The test involved randomly selecting n = 15 cigarettes, measuring the nicotine content (in milligrams) of each cigarette. The data is given below. 1:7;1:6;1:8;2:0;1:4;1:4;1:9;1:6;1:3;1:5;1:2;1:4;1:7;1:2;1:5 Assume that the nicotine content in each cigarette varies, which can be modeled by the Normal distribution. (a) Choose the correct statistical hypotheses. A. H0 : X = 1:4; HA : X < 1:4 B. Ho : μ = 1.4 Ha : μ > 1. 4 C. H0 : X > 1:4; HA : X < 1:4 D. H0 : X = 1:4; HA : X 6= 1:4 E. H0 : μ = 1:4; HA : μ 6= 1:4

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