Question

A study analysed data on all suspected cases of a new virus in a certain city within the past month. The analysis collected data on whether the suspected cases have worn a mask in the past month prior to the test for the new virus and the corresponding test results. The data are then summarised as follows:

Test Result Positive Negative Total

Not Wearing Mask 105 175 280

Wearing Mask 20 575 595

Total 125 750   875

(a) Using a Chi-square test at 5% level of significance to test the claim that wearing a mask is related to the number of positive test results for the new virus. (b) Construct a 95% confidence interval for the difference in the true percentage of positive test results between wearing a mask and not wearing a mask.

(c) Based on the results in part (a) and part (b), draw a conclusion on whether you are convinced to wear a mask in order to reduce the risk of getting a positive test result for the new virus?

Answer 1

(a). The given data is

Observed	Test Result	Total
Positive	Negative
Wearing a Mask	20	575	595
Not wearing a mask	105	175	280
Total	125	750	875

We know that the statistic is

where are the Observed and expected frequencies.   is given by where is the ith Row Total, is the jth Column total and T is the grand Total. We shall now form the Expected cell frequencis.

the expected frequencis

Expected	Test Result	Total
Positive	Negative
Wearing a Mask	85	510	595
Not wearing a mask	40	240	280
Total	125	750	875

. the critical value of at 5% level for 1 df is 3.841. Since the calculated value is higher thann the tabulated value, we reject the Null hypothesis.

Hence we conclude that  wearing a mask is related to the number of positive test results for the new virus.

(b). We have the data as :

Number of people wearing a mask and number of positive cases so

People not wearing masks   and number of positive cases so

The 95% confidence interval for the difference in proportion

The 95% confidence interval for the difference in proportion is (-0.40,-0.28).  

(c). We can see that the confidence interval doesn't include zero and hence the difference is signiifcant towards the negative side indicating that the proportion of positive cases is less for those wearing a mask compared to the proportion of positive cases for those who don't wear mask. Yes, I am convinced that wearing mask always reduce the chances of getting infected.