A study conducted in a certain period of time found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again. Suppose that the hiring intentions of the respondents were as follows: 32% selected Hire 29% selected Likely to Hire 21% selected Hire Uncertain 18% selected Do Not Hire Six month later, a random sample of 100 employers were asked about their hiring intentions and gave the following responses: 29 selected Hire 35 selected Likely to Hire 14 selected Hire Uncertain 22 selected Do Not Hire At 1% significance level, does it mean that proportions from the initial study have significantly changed? Use Goodness-of-Fit test and χ2χ2 distribution.
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.
A study conducted in a certain period of time found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again. Suppose that the hiring intentions of the respondents were as follows:
- 32% selected Hire
- 29% selected Likely to Hire
- 21% selected Hire Uncertain
- 18% selected Do Not Hire
Six month later, a random sample of 100 employers were asked about their hiring intentions and gave the following responses:
- 29 selected Hire
- 35 selected Likely to Hire
- 14 selected Hire Uncertain
- 22 selected Do Not Hire
At 1% significance level, does it mean that proportions from the initial study have significantly changed?
Use Goodness-of-Fit test and χ2χ2 distribution.
For part (a), round your answers in the " (O−E)2E(O-E)2E" column to 3 decimal places.
(a) Fill in the table below.
|
Hiring Intention |
Observed Frequency OO | Expected Frequency EE | O−EO-E | (O−E)2(O-E)2 | (O−E)2E(O-E)2E |
| Hire | 29 | ||||
| Likely to Hire | 35 | ||||
| Hire Uncertain | 14 | ||||
|
Do Not Hire |
22 | ||||
|
Total |
χ2=∑(O−E)2E=χ2=∑(O-E)2E= |
(b) State the null and alternative hypotheses, and identify which one is the claim.
H0H0:
H1H1:
Which one is the claim?
- H1H1
- H0H0
(c) Enter the number of degrees of freedom df=df=
For part (d), round your answer to 3 decimal places.
(d) What is the critical value χ2cr=χcr2=
(e) Is the null hypothesis rejected? Is the alternative hypothesis supported?
- Fail to reject H0H0 and fail to support H1H1 (claim)
- Reject H0H0 and support H1H1 (claim)
- Reject H0H0 (claim) and fail to support H1H1
- Fail to reject H0H0 (claim) and support H1H1
(f) Select the correct statement.
- At 1% significance level, there is not sufficient sample evidence to support the claim that proportions from the initial study have significantly changed.
- At 1% significance level, there is sufficient sample evidence to support the claim that proportions from the initial study have significantly changed.
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