Please solve both parts ### Do You Think You Smell?If you falsely believe you emit an unpleasant, foul, or offensive body odor, you may suffer from olfactory reference syndrome (ORS). This disorder disables patients, who often isolate themselves and consider suicide. Psychiatrists disagree over how prevalent ORS is in the human population.A study published in *Depression and Anxiety* (June 2010) discussed a self-reported survey of 2,481 university students in Japan. The study reported that 52 of the students were "concerned with emitting a strange bodily odor."#### Question**a.** Use the survey results to estimate the true proportion of all people in the world who suffer from ORS. Place 95% confidence bounds around the estimate and interpret the result. **Question:**b. Give several reasons why the inference, part a, may be invalid. Explain.---This prompt asks students to critically analyze an inference made in the previous part (not shown here). Students should identify potential logical fallacies, incorrect assumptions, or other factors that could contribute to the inference being invalid. The explanation should detail how each identified reason impacts the validity of the inference.

The value of z at 95% confidence level is 1.96, which can be obtained by using the standard normal table. The sample proportion is computed as follows, The corresponding confidence interval is computed as shown below: Therefore, the 95% confidence interval for the population proportion is 0.015<p<0.027, which indicates that we are 95\%95% confident that the true population proportion p is contained by the interval (0.015,0.027).(b) The assumption of calculating the confidence interval is that the confidence interval should be randomly selected from the population of interest and distribution should be normal. As the sample is selected from the students from the University of Japan, the result obtained from this sample will not represent the proportion of people in the whole world. To represent the whole world through the confidence interval, one should select the sample from all over the world, not from the students of Japan only. Hence, the results of part (a) will be invalid. Another reason that these results are not valid that students did not provide the method of selection of the sample. Hence, we cannot rely on the results of part (a).