Is there a difference in preference for free-range eggs across age groups? In order to develop marketing strategies, egg suppliers are interested in what type of customers only bought eggs produced in either free-range or caged conditions. Surveys were conducted at multiple retail outlets. The results are summarised in the table below. Below 30 30-49 50-65 Over 65 Total Free range 15 24 17 15 71 Caged 4 11 13 21 49 Total 19 35 30 36 120 a) When testing a null hypothesis of no association between the two factors in this contingency table, what would be the contribution to the test statistic from the ‘Caged and Below 30’ cell? b) Is there any evidence from this data that type of eggs bought is related to age group? Provide appropriate hypotheses, decision rule and conclusion for this test at the 5% significance level based on a test statistic of 8.999. Address any assumptions or necessary conditions in your analysis. If you find evidence of an association between the variables, describe it. c) Use this data to construct a 90% confidence interval for the proportion of this population who only buy caged eggs. Provide a meaningful interpretation of your interval.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Is there a difference in preference for free-
| Below 30 | 30-49 | 50-65 | Over 65 | Total | |
| Free range | 15 | 24 | 17 | 15 | 71 |
| Caged | 4 | 11 | 13 | 21 | 49 |
| Total | 19 | 35 | 30 | 36 | 120 |
a) When testing a null hypothesis of no association between the two factors in this contingency table, what would be the contribution to the test statistic from the ‘Caged and Below 30’ cell?
b) Is there any evidence from this data that type of eggs bought is related to age group? Provide appropriate hypotheses, decision rule and conclusion for this test at the 5% significance level based on a test statistic of 8.999. Address any assumptions or necessary conditions in your analysis. If you find evidence of an association between the variables, describe it.
c) Use this data to construct a 90% confidence interval for the proportion of this population who only buy caged eggs. Provide a meaningful interpretation of your interval.
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