Data was collected from a simple random sample of 200 cell phone users age 18 or older in the United States. Each user was categorized by age-group and by whether he or she uses a certain cell phone app. The table shown summarizes the data, with expected cell counts in parentheses. Uses Cell Phone App Yes No Total Young Adults 4 (15.2) 76 (64.8) 80 Older Adults 29 (19.38) 73 (82.62) 102 Age-Group Elderly Adults 5 (3.42) 13 (14.58) 18 Total 38 162 200 Which statement is true about whether the conditions for a chi-square test for independence have been met? All necessary conditions are satisfied to apply a chi-square test for independence between age-group and texting use by cell phone users. в The data from the different age-groups are not the result of independent random samples; therefore, the conditions for the test are not met. The total sample size in one or more of the age-groups too small to meet the conditions of the chi-square test for independence. Not all of the observed cell counts are large enough to satisfy the conditions for the chi-square test for independence. Not all of the expected cell counts are large enough to satisfy the conditions for the chi-square test for independence.
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.
Data was collected from a simple random sample of 200 cell phone users age 18 or older in the United States. Each user was categorized by age-group and by whether he or she uses a certain cell phone app. The table shown summarizes the data, with expected cell counts in parentheses.
| Uses Cell Phone App | ||||
| Yes | No | Total | ||
| Age-Group | Young Adults | 4 (15.2) | 76 (64.8) | 80 |
| Older Adults | 29 (19.38) | 73 (82.62) | 102 | |
| Elderly Adults | 5 (3.42) | 13 (14.58) | 18 | |
| Total | 38 | 162 | 200 |
Which statement is true about whether the conditions for a chi-square test for independence have been met?
-
All necessary conditions are satisfied to apply a chi-square test for independence between age-group and texting use by cell phone users.
All necessary conditions are satisfied to apply a chi-square test for independence between age-group and texting use by cell phone users.A -
The data from the different age-groups are not the result of independent random samples; therefore, the conditions for the test are not met.
The data from the different age-groups are not the result of independent random samples; therefore, the conditions for the test are not met.B -
The total
sample size in one or more of the age-groups is too small to meet the conditions of the chi-square test for independence.The total sample size in one or more of the age-groups is too small to meet the conditions of the chi-square test for independence.C -
Not all of the observed cell counts are large enough to satisfy the conditions for the chi-square test for independence.
Not all of the observed cell counts are large enough to satisfy the conditions for the chi-square test for independence.D -
Not all of the expected cell counts are large enough to satisfy the conditions for the chi-square test for independence.
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