In 2011, the number of text messages sent and received by teenage girls (ages 12

Question

In 2011, the number of text messages sent and received by teenage girls (ages 12-18) was strongly right skewed. The mean number of messages sent and received each day was 165 with a standard deviation of 45 messages. Suppose we assume teenage boys (ages 12 - 18) send and receive the same number of messages daily. Completely describe the sampling distribution of the sample mean number of text messages sent and received when samples of 273 teenage boys are selected. a. mean: H_ standard deviation: ?9- shape: the distribution of J ?s Select an answer (round your answer to 4 decimal places) -because Select an answer Using the distribution described in part a, what is the probability of observing a sample mean of 159.637 or less? b. (round to 2 decimal places) ° z = o probability OThe probability would be classified as large O The probability would be classified as small. (include 4 decimal places) c. Classify the probability found in part b using the rule of thumb discussed in class. d. Based on the probability found, what conclusion can be reached? There Select an answer suficient evidence to conclude the mean number of text messages sent by male teenagers is [Select an answer 165.

Explanation / Answer

a)
mean = 165 ,
std.dev. = 45/sqrt(273) = 2.7235

shape of sampling distribution is normal because sample size is larger.

b)

P(X < 159.637)

z = ( x - mean) /(s/sqrt(n))
= ( 159.637 - 165)/(45/sqrt(273))
= -1.97

P(X < 159.637) = P(z < -1.9691) = 0.0245 by using standard normal table

c)
The probability would be classified as small

d)
There is sufficient evidence to conclude that the mean number of text messages sent by male teenagers is greater than 165

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