The average height and weight of women varies around the world, but in the United States in 2010, the average adult female height was 63.8 inches (approximately 5 feet 4 inches) and 166.2 pounds, according to the Centers for Disease Control and Prevention. It is believed that women from the Midwest are taller as compared to other regions. We want to test this claim and we use the Getting To Know You Survey data to support the claim that average height of Minnesotan women enrolled in University of Minnesota is greater than 63.8 inches? Test at a = 0.05.You may find the following code helpful to extract the height variable for US women:NoU attach(NoU)height_F.Mn (a) State the parameter of interest.(b) Give assumptions for the statistical test. Discuss if the assumptions will be met for the problem.(c) State H0 and Ha.(d) Use t.test() command to calculate the test statistic and the p-value. Copy and paste your R results into your assignment.(e) State your conclusion, and interpret it in the context of the problem.(f) Repeat the test (using t.test()) but this time you are testing whether the average height of Minnesotan women enrolled in University of Minnesota is not equal to 63.8 inches?(g) State the 95% confidence interval that you obtained from the output of part f. Does it agree with your conclusion in part f? Explain.
2. Consider the hypothesis test in the R problem 1 above. (a) What would the p-value be if you were testing whether the average height of Minnesotan women enrolled in University of Minnesota is less than 63.8 inches? (b) What does type I error mean in the context of this problem? (c) What does type II error mean in the context of this problem? (d) Given your conclusion in the R problem 1 part e), which type of error could you have made? Explain.

 

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