Question

How common are financial cost or contractual constraints associated with smartphone​ ownership? A survey of smartphone users found that 50​% of the​ 18- to​ 29-year-olds, 40​% of the​ 30- to​ 49-year-olds, 26​% of the​ 50- to​ 64-year-olds, and 17​% of those age 65 or older have reached the maximum amount of data they are allowed to use as part of their​ plan, at least on​ occasion: Suppose the survey was based on 300 smartphone owners in each of the four age​ groups: 18 to​ 29, 30 to​ 49, 50 to​ 64, and 65 and older. Complete parts​ (a) through​ (c).

a. At the 0.05 level of​ significance, is there evidence of a difference among the age groups in the proportion of smartphone owners who have reached the maximum amount of data they are allowed to use as part of their​ plan, at least on​ occasion?

State the null and alternative hypotheses.

The test statistic is X^2stat=

The critical value for this test is

b. Determine the​ p-value in​ (a) and interpret its meaning.

Answer 1

we have given : n=300 Age ". Frequency. 18-29 50%. 30-49 401. - 50-64 265. 65 ory its. | 133). d) At the gros level of significance, claim: - is there evidence to a difference among the age group in the proportion of smartphone

owners who have reached the maximum amount of data . they are allowed to use as part of their plan at least on occasion 2 among the To test : Ho: There is no difference age group rs H: There is evidence to difference the age group . test statistic i x? El0;-Ej2 among where O;= observed & E= Expected frea

E= expected frequency= (50%+ 40%. +26%. Hits] =123 33.25.7.) X = 650 - 3325)2 + (40-37.25)2+(26-33.25)2+ (17-3325123 33.25. = [280.5625 + 45.5625 + 52.5625 + 264.0625] 33.25 642.75 33.25 a 19. 3308

k= 4 . df = K-=3. critical value = tais = 7.815 ] (from table) Decision - we reject to at Clod) NOD Y level of significance if chi-square (x²) rest statistic value > x² critical value here x2 > K², of we reject Ho. There is age group in the who have reached the evidence to difference among the proportion of smart phone owners maximum amount of data

O p value probability of rejecting Ho when It is true. pl i test of ahisticl > Critical calue] here. p. value=0.000 234 using p value approach we reject Ho when it is true here we here p value ca value hence reject Ho at 120.us same for critical value of p value] [ result are