Suppose that, over a certain period of time, a parent monitors how many texts th

Question

Suppose that, over a certain period of time, a parent monitors how many texts their 17 year old son sends each day. The average amount of texts sent a day is 42, and the standard deviation is 12. (a) If one day from this time period is randomly selected, and the number of texts for that day is one standard deviation above the population mean, how many texts were sent that day? 54] (whole number) Now, suppose random samples of 16 days are selected during this time period, and for each sample, the sample mean is calculated. (b) What is the mean of the sampling distribution of the sample mean? (No Response)42 (whole number) (c)What is the standard error of the sampling distribution of the sample mean? No Response)3 (whole number) (d) If, for a random sample of 16 days, the sample mean ends up being exactly one standard error above the population mean, what is the sample mean for those 16 days? No Response[45] (whole number) (e) Suppose a random sample of 16 days had a sample mean of 36 text messages a day, how many standard errors belovw the population mean would that be? No Response) 2 (whole number)

Explanation / Answer

Easy! Here are the answers with calculations:

a. 1 deviation above mean is Mean + 1*deviation = 42+1*12 = 54

b. Mean of sample is equal to mean of population = 42

c. Standard error = standard deviation / sqrt(n), where n is sample size = 12/sqrt(16) = 3

d. 1 deviation above sample mean is therefore = Sample Mean + 1*Sample deviation = 42+3 = 45

e. 36 = 42+x*3 ( since 3 is the standard error). x = -2, So, it is 2 std errors below the population mean

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