Question

10.90 According to a Johns Hopkins University study published in the American Journal of Public Health, widows live longer than widowers. Consider the following survival data collected on 100 widows and 100 widowers following the death of a spouse Years Lived Widow Widower Less than 5 5 to 10 More than 10 25 42 Can we conclude at the 0.05 level of significance that the proportions of widows and widowers are equal with respect to the different time periods that a spouse survives after the death of his or her mate?

can it be done without using excel??

Answer 1

The full answer is in detail below. let me know in case you've doubts about the answer.

Here' is the contingency table below.

It has the following information : the observed cell totals, (the expected cell totals) and [the chi-square statistic for each cell].

The hypothesis set is defined as:

Ho: Proportions of widows and widowers are equal

Ha: Proportions of widows and widowers are NOT equal

Results
	Widow	Widower				Row Totals
Less than 5	25  (32.00)  [1.53]	39  (32.00)  [1.53]				64
5 to 10	42  (41.00)  [0.02]	40  (41.00)  [0.02]				82
More than 10	33  (27.00)  [1.33]	21  (27.00)  [1.33]				54
Column Totals	100	100				200  (Grand Total)

The chi-square statistic is 5.7779. The p-value is .055633. The result is not significant at p < .05.

Answer: Hence, we conclude that "Proportions of widows and widowers are equal" since the test of Chi-Square reveals a p-value of more than .05 i.e. the 2 factors are independent of each other.