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ANSWER USING R CODE Using the dataset 'LakeHuron' which is a built in R dataset describing the...

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Basic Math

ANSWER USING R CODE

Using the dataset 'LakeHuron' which is a built in R datasetdescribing the level in feet of Lake Huron from 1872- 1972. Toassign the values into an ordinary vector,x, we can do thefollowing 'x <- as.vector(LakeHuron)'. From there, we can accessthe data easily. Assume the values in X are a random sample from anormal population with distribution X. Also assume the X has anunknown mean and unknown standard deviation. With this informationin mind, answer the following.

a) The sample mean of x

b) the sample mean of 8X

c) Using this data, create a 97% confidence interval for X usingthe a t-distribution critical value tstar.

d) Using this data, create a 3 percent level test of H0:mu =578.9 versus the alternative Ha:mu > 578.9. USing tisinformation, calculate the value of the z-statistic

e) With the z-statistic, calculate the appropriate p-value.

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