Question

In Africa in 2011, the number of deaths of a female from cardiovascular disease for different age groups are in the table below ("Global health observatory," 2013). In addition, the proportion of deaths of females from all causes for the same age groups are also in table below.

Table: Deaths of Females for Different Age Groups

Age	5-14	15-29	30-49	50-69	Total
Cardiovascular Frequency	8	16	56	433	513
All Cause Proportion	0.10	0.12	0.26	0.52

Do the data show that the death from cardiovascular disease are in the same proportion as all deaths for the different age groups? Test at the 5% level.

(i) Which of the following statements correctly defines the null hypothesis H_O?

A. Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups

B. Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups

C. neither of these statements is correct for H_O

Enter letter corresponding to correct answer

(ii) Which of the following statements correctly defines the alternate hypothesis H_A?

A. Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups

B. Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups

C. neither of these statements is correct for H_A

Enter letter corresponding to correct answer

(iii) Enter the level of significance ? used for this test:

Enter in decimal form. Examples of correctly entered answers:  0.01    0.02    0.05    0.10

  (iv) Are any of the expected frequency values (for which H_O is true) for any cell in your table less than 5? Calculate the expected frequencies using technology, the select most correct answer:

A. yes - this will not affect results of hypothesis test

B. yes - this may invalidate results of hypothesis test

C. no - this will not affect results of hypothesis test

D. no - this may invalidate results of hypothesis test

Enter letter corresponding to correct answer. Recommend using (Chi-Square Goodness-of-Fit Applet) to create contingency table of expected and observed frequency values in order to answer this question. BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

(v) Using calculator, spreadsheet, or online calculator, determine test statistic:

Enter value in decimal form rounded to nearest thousandth. Examples of correctly entered answers:

2.010   0.307        1.600        11.019

Recommended online calculator:  Chi-Square Goodness-of-Fit Applet

BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

(vi) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.

Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers:

0.0001     0.0021     0.0305     0.6004      0.8143    1.0000

Recommended online calculator:  Chi-Square Goodness-of-Fit Applet

BE SURE when entering expected frequency data you select what format you're entering the data ("percent expected", "fraction expected" which includes decimal, or "actual number expected").

(vii) Comparing p-value and ? value, which is the correct decision to make for this hypothesis test?  

A. Reject H_o

B. Fail to reject H_o

C. Accept H_o

D. Accept H_A

Enter letter corresponding to correct answer.

  (viii) Select the statement that most correctly interprets the result of this test:

A. The result is not statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

B. The result is statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

C. The result is not statistically significant at .05 level of significance. There is not enough evidence to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

D. The result is statistically significant at .05 level of significance. There is not enough evidence to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups.

Enter letter corresponding to most correct answer

Answer 1

(i) Deaths from cardiovascular disease in females are in the same proportion as all deaths for the different age groups (Option B)

?This is the null hypothesis statement

(ii) Deaths from cardiovascular disease in females are not in the same proportion as all deaths for the different age groups (Option B)

?This is the alternate hypothesis statement

(iii) 0.05

We are already given alpha value of 5% in problem statement

(iv)  no - this will not affect results of hypothesis test (Option C)

The expected frequencies should not be less than 5 for obtaining a valid test statistic in Chi-square test. However, as will be seen below in table, none of these frequencies is less than 5.

(v)  The Chi-square statistic is calculated using the formula

where O and E are the observed and expected frequency values. This can be tabulated as

Age	Cardiovascular Frequency (O)	All Cause Proportion	Expected Frequency (E)	Chi-Square Calculation
5-14	8	0.1	51.3	36.54756335
15-29	16	0.12	61.56	33.71854451
30-49	56	0.26	133.38	44.89177088
50-69	433	0.52	266.76	103.5977568
Total	513			218.7556355

(vi) The degrees of freedom for the test are 3, since there are 4 values in table. The p-value, using any software or calculator is zero.

(vii) Reject H₀(Option A)

As p-value is practically zero, viz. a highly significant result, so we must reject the null hypothesis

(viii)  The result is statistically significant at .05 level of significance. Sufficient evidence exists to support the claim that deaths from cardiovascular disease in females are not in the same proportion as all deaths of females for the different age groups. (Option B)