Statistical Hypothesis Testing and Inference: A Comprehensive Assignment

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Statistical Hypothesis Testing and Inference: A ComprehensiveAssignment1. (1 pt) An agricultural field trial compares the yield of two varieties of corn. The researchersdivide in half each of 19 fields of land in different locations and plant eachcorn variety in onehalf of each plot. After harvest, the yields are compared in bushels per acre at each location. The19 differences (Variety A-Variety B) give ¯ x = 2:27 and s = 4:49. Does this sample provideevidence 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 themean is greater than 1, mu < 1 for the mean is less than 1, mu not = 1 for the mean is not equal to1)( Hint: Use the only equal sign in the null hypothesis)Ho:mu1-mu2=0:Ha:mu1-mu2>0:(b) Find the value of the test statistic. Use two decimal places.n=19, test stat : t= 2.27/4.49/sqrt(19) =2.20p-vlue=.0204 df=18(c) Answer the question: Does this sample provide evidence that Variety A had a higher yieldthan Variety B? (Use a 5% level of significance) (Type: Yes or No)YesAnswer(s) submitted:2. (1 pt) Credit scores are used by banks, financial institutions, and retailers to determine one’strustworthiness, and their ability to pay their credit card, when he/she is given a credit card. Thehigher 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 ofCanadians between the ages of 25 to 40 has dropped. Prior to the current economic downturn, themean 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 determinedusing 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= 673B. H0 : X > 673; HA : X < 673C. H0 : X = 673; HA : X < 673D. H0 : μ > 673; HA : μ < 673E. H0 : X = 673; HA : X 6= 673F. H0 : μ = 673 HA : μ < 673(b) Determine the value of the test statistic for this test, usetwo decimals in your answer.Test Statistic =t =(650.75-673)/(41.87/sqrt(20))=-2.38(c) Determine the P-value for thistest, to three decimal places.p-value=.014(d) Based on theabove calculations, we shouldrejectthe nullhypothesis. Use alpha = 0.05

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