The following Table contains information from a survey among 599 participants classified according t

Maurice Maldonado

Maurice Maldonado

Answered question

2022-04-21

The following Table contains information from a survey among 599 participants classified according to their age groups. The second column shows the percentage of obese people per age class among the study participants. The last column comes from a different study at the national level that shows the corresponding percentages of obese people in the same age classes in the UK. Perform a Hypothesis test at the 5% significance level to determine whether the survey participants are a representative sample of the UK obese population.
 Age Class (Years)  Obese (Percentage)  Expected UK average (percentage) 203065.032.6314026.532.6415013.636.6516021.936.6617021.039.7

Answer & Explanation

mandamosppy

mandamosppy

Beginner2022-04-22Added 21 answers

Chi-Square Test: In statistical hypothesis test, a chi-square test, or specifically Pearson's chi-square test is performed when the test statistic is distributed as chi-square under the null hypothesis. This test is used to determine whether there is a significant difference between the observed and the expected frequencies in one or more categories of a contingency table.
In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis is true i.e. there are no significant differences between the classes in the population, the test statistic which is computed from the observations follows a chi-square frequency distribution. The purpose of the test is to determine how likely the observed frequencies would be assuming the null hypothesis is true.
If Oi and Ei be the observed and expected frequency for the ith category, then the chi-square test statistic is given by,
χc2=i(OiEi)2Ei
where c is the degrees of freedom of the chi-square distribution.
 Age Class (Years)  Obese (Percentage) (Oi) Expected UK average (percentage) (Ei)(OiEi)2/Ei203065.032.632.20314026.532.61.14415013.636.614.45516021.936.65.90617021.039.78.81 Total 148.0178.162.51
Here,
χc2=i(OiEi)2Ei
=62.51 (rounded to 2 decimal places)
Here the degrees of freedom is 5-1=4 and the value of α=5%=0.05.
Therefore, the tabulated value of chi-square is
χ{0.05.4}2=9.488
Clearly,
χc2>χ{0.05.4}2
Therefore, we reject the null hypothesis at 0.05 level of significance.
Conclusion: At 5% level of significance, there is not enough evidence to support the claim that the survey participants are a representative sample of the UK obese population.

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