Question

16) Two computer users were discussing tablet computers. A higher proportion of people ages 16 to 29 use tablets than the proportion of people age 30 and older. The table below details the number of tablet owners for each age group. Test at the 1% level of significance. (For subscripts let 1 = 16-29 year old users, and 2 = 30 years old and older users.)

	16–29 year olds	30 years old and older
Own a Tablet	69	231
Sample Size	630	2,314

NOTE: If you are using a Student's t-distribution for the problem, including for paired data, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

• Part (c)
  In words, state what your random variable P'1 − P'2 represents.

• P'1 − P'2 represents the difference between the average numbers of 16-29 year old tablet users from that of the 30 years old and older tablet users.

• P'1 − P'2 represents the difference between the proportions of 16-29 year old tablet users from that of the 30 years old and older tablet users.    

• P'1 − P'2 represents the difference between the average proportions of 16-29 year old tablet users from that of the 30 years old and older tablet users.

• P'1 − P'2 represents the average difference between the proportions of 16-29 year old tablet users from that of the 30 years old and older tablet users.

• Part (d)
  State the distribution to use for the test. (Round your answers to four decimal places.)
  P'1 − P'2bExp H N B P ?

• Part (e)
  What is the test statistic? (If using the z distribution round your answer to two decimal places, and if using the t distribution round your answer to three decimal places.)
  z =

• Part (f)
  What is the p-value? (Round your answer to four decimal places.)
  
  
  (f ii)Explain what the p-value means for this problem.

• If H0 is true, then there is a chance equal to the p-value that the proportion of tablet users that are 16-29 year old users is 0.01 less than the proportion of tablet users that are 30 years old and older tablet users.

• If H0 is true, then there is a chance equal to the p-value that the proportion of tablet users that are 16-29 year old users is at least 0.01 more than the proportion of tablet users that are 30 years old and older tablet users.    

• If H0is false, then there is a chance equal to the p-value that the proportion of tablet users that are 16-29 year old users is at least 0.01 more than the proportion of tablet users that are 30 years old and older tablet users.

• If H0 is false, then there is a chance equal to the p-value that the proportion of tablet users that are 16-29 year old users is 0.01 less than the proportion of tablet users that are 30 years old and older tablet users.

• Part (g)
  Sketch a picture of this situation. Label and scale the horizontal axis and shade the region(s) corresponding to the p-value

Answer 1

Corret option is:

P'1 − P'2 represents the difference between the proportions of 16-29 year old tablet users from that of the 30 years old and older tablet users.    

(d)

and

Hence, the distribution to use for the test is

(e)

(f)(i)

(ii)

If H0 is true, then there is a chance equal to the p-value that the proportion of tablet users that are 16-29 year old users is at least 0.01 more than the proportion of tablet users that are 30 years old and older tablet users.    

(g)

Following is the sletch:

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