On occasion, medical studies need to model the proportion of the population that has a disease and compare that to observed frequencies of the disease actually occurring. Suppose the end-stage renal failure in south-west Wales was collected for different age groups. Do the data in the table show that the observed frequencies are in agreement with proportion of people in each age group? Test at the 1% level. Renal Failure Frequencies Age group 16-29 30-44 45-59 60-74 75+ Total Observed Frequencies 125 152 134 124 48 583 Expected Proportion 0.23 0.25 0.22 0.21 0.09 State the hypotheses. H0: The observed frequencies in agreement with proportion of people in each age group. Ha: The observed frequencies in agreement with proportion of people in each age group. Calculate the χ2 test statistic. Round expected values to two decimal places. Round χ2 to 3 decimal places. χ2 = Calculate the p-value. Round to 3 decimal places. p-value = State your decision. Since p-value α, H0. Interpret the results. At the 5% signficance level there enough evidence to conclude that the observed frequencies in agreement with proportion of people in each age group.
On occasion, medical studies need to model the proportion of the population that has a disease and compare that to observed frequencies of the disease actually occurring. Suppose the end-stage renal failure in south-west Wales was collected for different age groups. Do the data in the table show that the observed frequencies are in agreement with proportion of people in each age group? Test at the 1% level.
Renal Failure Frequencies
| Age group | 16-29 | 30-44 | 45-59 | 60-74 | 75+ | Total |
|---|---|---|---|---|---|---|
| Observed Frequencies | 125 | 152 | 134 | 124 | 48 | 583 |
| Expected Proportion | 0.23 | 0.25 | 0.22 | 0.21 | 0.09 |
State the hypotheses.
H0: The observed frequencies in agreement with proportion of people in each age group.
Ha: The observed frequencies in agreement with proportion of people in each age group.
Calculate the χ2 test statistic. Round expected values to two decimal places. Round χ2 to 3 decimal places.
χ2 =
Calculate the p-value. Round to 3 decimal places.
p-value =
State your decision.
Since p-value α, H0.
Interpret the results.
At the 5% signficance level there enough evidence to conclude that the observed frequencies in agreement with proportion of people in each age group.
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