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In a particular neighbourhood of a city, the following contingency table shows whether or not residents do physical exercise regularly and eat sugary food.
Exercise regularly Does not exercise regularly Total
Eat sugary food 50 73 123
Does not eat sugary food 69 77 146
Total 119 150 269
Complete the details of the following chi-square hypothesis test of H0: Regular exercise and eating sugary food are independent versus HA: Regular exercise and eating sugary food are dependent/associated.
a. Calculate the expected counts for each combination under the null hypothesis. Express your answers rounded to two decimal places and do not include any calculations.
Exercise regularly Does not exercise regularly
Eats sugary food
Does not eat sugary food
b. Use the observed counts in the data table in the question and the expected counts from part (a) to calculate the chi-square test statistic. Express your answer to two decimal places and do not include any calculations.
c. How many degrees of freedom are needed for the chi-square test?
d. The 95th percentile of a chi-square distribution with 1 degree of freedom is 3.84. Therefore, based on a significance level
$$\alpha = 0.05$$, we:
Reject H0 in favour of HA
Fail to reject H0
e. An appropriate conclusion for the study is:
There is sufficient evidence regular exercise and eating sugary food are dependent/associated.
There is insufficient evidence regular exercise and eating sugary food are dependent/associated.