Question

# A random sample of n = 500 books is selected from a library and the number...

A random sample of n = 500 books is selected from a library and the number of words in the title of each book is recorded. The sample mean number of words in the title is 6.2 words. The population variance is 40 words^2 .

Please show how to do each one using R and Rstudio.

a) (2 points) Compute the z-statistic for testing the null hypothesis H0 : µ = 7.

b) (3 points) Perform a level ? = 0.1 test of H0 : µ = 7 vs. the one-sided lesser alternative HA : µ < 7.

c) (2 points) What is the one-sided lesser p-value for the statistic you computed in part a)?

d) (2 points) What is the two-sided p-value for the statistic you computed in part a)?

e) (2 points) Construct a 95% confidence interval for the population mean number of words per title. Hint: recall that a 95% confidence interval is formed by the sample mean ±1.96× standard deviation of the sampling distribution.

f) (1 point) Based on your confidence interval from part e), would a level ? = 0.05 two-sided hypothesis test reject or fail to reject the null hypothesis that the population mean is 6.5 words per title?

a) Given H0 : µ = 7.   HA : µ not = 7

b) Given level ? = 0.1

Test for H0 : µ = 7 vs. the one-sided lesser alternative HA : µ < 7

c)

P-value = 0.00234

Here p-value < alpha ( = 0.1 ) so we reject H0

thus we conclude that µ < 7

d) P-value = 0.0047

Here p-value < alpha ( = 0.1 ) so we reject H0

thus we conclude that µ not = 7

e)

f)

Population mean µ (=7) is not in the above 95% confidence interval so we reject H0

Thus we conclude that Population mean  µ not =7

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