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Two computer users were discussing tablet computers. A higher proportion of people aga 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 signicance. [For subscripts let 1 - 16-29 year old users, and 2 - 30 years old and older users.) 16-29 year olds 3|] years old and older Own a Tablet 69 231 Sample Size 626 2,307 NOTE: IF you are using a Student's tdistribution 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.) El m (a) State the null hypothesis. 0 Ho: P1 ' P2 0 Ho: P1
P2 O \".1 P1 ' P2 El em [6) In words. state what your random variable P". '2 represents. 0 P1 7 P2 represents the average difference between the proportions of 16-29 year old tablet users from that ofthe 30 years old and older tablet users. 0 P1 7 P2 represents the difference between the average numbers of 1629 year old tablet users from thatof the 30 years old and older tablet users. 0 P1 P2 represents the difference between the average proportions of 1629 year old tablet users from that ofthe 30 years old and older tablet users. 0 P1 P2 represents the difference between the proportions of 1529 year old tablet users from that ofthe 30 years old and older tablet users. El FIR It'll State the distribution to use for the test. (Round your answers to four decimal places.) P'VP'Z J? ( . ) N : H a m to) E\" a What is lhh'mm'lic? [lt using the z distribution round your answer to two decimal places. and it using the t'distribution round your answertothree decimal places.) ---Sslsr:t--- a = EIFIi What is the pvalue? {Round your answer to four decimal places.) Explain what the pvalue means for this problem. 0 If H0 is false. then there is a chance equal to the pyalue that the proportion of tablet users that are 1529 year old users is at least 0.01 more than the proportion ot tablet users that are 30 years old and older tablet users. 0 If H0 is false. then there is a chance equal to the pyalue that the proportion of tablet users that are 1029 year old users is 001 less than the proportion ot tablet users that are 30 years old and older tablet users. 0 If H0 is true. then there is a chance equal to the pvalue that the proportion of tablet users that are 1629 year old users is 0.01 more than the proportion of tablet users that are 30 years old and older tablet users. 0 If H0 is true. then there is a chance equal to the pvalue that the proportion of tablet users that are 1629 year old users is at least 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. 1/2(p-value) 1/2(p-value) P-value P'1 - P'2 C 0 P'1 - P'2 C 0 1/2(p-value) 1/2(p-value) p-value P'1 - P'2 P'1 - P'2 0 C 0El Part [I11 Indicate the conect decision ['reject" or \"do not reject' the null hypothesis). the reason for itl and write an appropriate conclusion. (it Alpha {Enter an exact number as an integer. fraction. or decimal.) a: (ii) Decision: 0 reject the null hypothesis 0 do not reject the null hypothesis (iii) Reason for decision: O Since pvelue a. we reject the null hypothesis. O Since |cvalue > an we do not reject the null hypothesis. (iv) Conclusion: O There is sufcient evidence to conclude that a higher proportion of tablet owners are aged 16 to 29 years old than are 30 years old and older. Q There is not sufcient evidence to conclude that a higher proportion 01 tablet owners are aged 16 to 29 years old than are 30 years old and older. Explain how you determined whim distribution to use. O The tdistribution will be used because the samples are dependent. O The standard normal distribution will be used because the samples are independent and the population standard deviation is known. O The [distribution will be used because the samples are independent and the population standard deviation is not known. O The standard normal distribution will be used because the samples involve the ditferenoe in proportions
