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? (whole number) (c)What is the standard error of the sampling distribution of the sample mean? (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? (whole number) (e) Suppose a random sample of 16 days had a sample mean of 36 text messages a day, how many standard errors below the population mean would that be? (whole number)

Answer 1

a) texts =42+12 =54

b) mean =42

c) std error =std deviation/(n)^1/2 =12/(16)^1/2 =3

d) sample mean =42+3 =45

e) number of std deviation below =(42-36)/3 =2