The director of student services at San Bernardino Valley College is interested in whether women are just as likely to attend orientation as men before they begin their coursework. A random sample of freshmen at San Bernardino Valley College were asked to specify their gender and whether they attended the orientation. The results of the survey are shown below: Data for Gender vs. Orientation Attendance Women Men Yes 422 529 No 267 268 Let p1p1 be the proportion of women who attended the orientation and p2p2 be the proportion of men who attended the orientation. What can be concluded at the αα = 0.10 level of significance? The p-value = (Please show your answer to 4 decimal places.) Based on this, we should Select an answer fail to reject accept reject the null hypothesis. Thus, the final conclusion is that ... A) The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population proportion of freshmen women at Oxnard College who attend orientation is the same as the population proportion of freshmen men at Oxnard College who attend orientation. B) The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of freshmen women at Oxnard College who attend orientation is different from the population proportion of freshmen men at Oxnard College who attend orientation. C) The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of freshmen women at Oxnard College who attend orientation is different from the population proportion of freshmen men at Oxnard College who attend orientation. D) The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the proportion of the 689 freshmen women who attended orientation is different from the proportion of the 797 freshmen men who attended orientation.
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.
The director of student services at San Bernardino Valley College is interested in whether women are just as likely to attend orientation as men before they begin their coursework. A random sample of freshmen at San Bernardino Valley College were asked to specify their gender and whether they attended the orientation. The results of the survey are shown below:
Data for Gender vs. Orientation Attendance
| Women | Men | |
|---|---|---|
| Yes | 422 | 529 |
| No | 267 | 268 |
Let p1p1 be the proportion of women who attended the orientation and p2p2 be the proportion of men who attended the orientation. What can be concluded at the αα = 0.10 level of significance?
- The p-value = (Please show your answer to 4 decimal places.)
- Based on this, we should Select an answer fail to reject accept reject the null hypothesis.
- Thus, the final conclusion is that ...
- A) The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population proportion of freshmen women at Oxnard College who attend orientation is the same as the population proportion of freshmen men at Oxnard College who attend orientation.
- B) The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population proportion of freshmen women at Oxnard College who attend orientation is different from the population proportion of freshmen men at Oxnard College who attend orientation.
- C) The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population proportion of freshmen women at Oxnard College who attend orientation is different from the population proportion of freshmen men at Oxnard College who attend orientation.
- D) The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the proportion of the 689 freshmen women who attended orientation is different from the proportion of the 797 freshmen men who attended orientation.
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