Chi-Square test Qs

#1
Hi there, I am practicing exam questions where we are presented with minitab outputs and have to answer questions. I have attempted all the questions below but I am unsure if all of them are correct.

Phenylthiocarbamide (PTC) is a chemical that tastes bitter to some people (“tasters”) and bland to everyone else (“non-tasters”), a response which is controlled by two forms of the TAS2R38 gene. A sample of individuals from across the world had their tasting status determined. The researchers were interested in i) estimating the proportion of living humans who are tasters and ii) to determine if there was an association between tasting status and whether the person lived in the northern or southern hemisphere. Use the relevant output below to answer the following questions.
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i) Estimate the proportion of individuals in the population who are tasters (i.e. can taste PTC).

73.24%

ii) Explain why there is evidence that the majority of the population of interest can taste PTC.

The 95% confidence interval does not contain zero, therefore the result is significant.

iii) State the appropriate null and alternative hypotheses for the Chi-square test carried out.

H0: There is no association between tasting status and whether the person lived in the northern or southern hemisphere.

H1: There is an association between tasting status and whether the person lived in the northern or southern hemisphere.

vi) Use the output to decide whether or not there was sufficient evidence of an association between tasting status and whether the person lived in the northern or southern hemisphere.

As the p value is 0.155 and greater than 0.05, we fail to reject the null hypothesis, therefore we conclude that there is no association between tasting status and whether the person lives in the northern or southern hemisphere.

vii) What are the assumptions underlying the chi-square test? Do they appear justified?

The assumptions of the Chi-square test include:

The data in the cells should be frequencies, or counts of cases rather than percentages or some other transformation of the data, and this is confirmed in the output provided.

The levels (or categories) of the variables are mutually exclusive. That is, a particular subject fits into one and only one level of each of the variables and this was confirmed in the fact that southern and northern hemispheres are mutually exclusive.

viii) Write a short conclusion.

While the majority (73.24%) of candidates in the sample (representing a worldwide population) were ‘tasters’, there appears to be no association between being a ‘taster’ or not and whether the person lived in the northern or southern hemisphere.