A random sample of 15 chemists from Washington state shows an average salary of $45720 with a standard deviation of $654. A random sample of 24 chemists from Florida state shows an average salary of $42403 with a standard deviation of $665. A chemist that has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At a=0.01 is this chemist correct? Let Washington be sample 1 and Florida be sample 2. The correct hypotheses are: O Ho: H1 < H2 HA: 41 > µ2(claim) O Ho: µ1 2 H2 HA: H1 < µ2(claim) O Ho: µ1 = µ2 HA: H1 + µ2(claim) Since the level of significance is 0.01 the critical value is 2.749 and -2.749 The test statistic is: |(round to 3 places) The p-value is: (round to 3 places) The decision can be made to: O reject Ho O do not reject Ho
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.
Question Three.
![**Hypothesis Testing for Chemist Salaries in Washington and Florida**
A random sample of 15 chemists from Washington state shows an average salary of $45,720 with a standard deviation of $654. A random sample of 24 chemists from Florida state shows an average salary of $42,403 with a standard deviation of $665. A chemist who has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At α = 0.01, is this chemist correct? Let Washington be sample 1 and Florida be sample 2.
**The correct hypotheses are:**
- \( H_0: \mu_1 = \mu_2 \)
- \( H_A: \mu_1 \neq \mu_2 \) (claim)
Since the level of significance is 0.01, the critical values are 2.749 and -2.749.
- **The test statistic is:** [blank] (round to 3 places)
- **The p-value is:** [blank] (round to 3 places)
The decision can be made to:
- \( \circ \) reject \( H_0 \)
- \( \circ \) do not reject \( H_0 \)
**The final conclusion is that:**
- \( \circ \) There is enough evidence to reject the claim that chemists in Washington make a different amount than chemists in Florida.
- \( \circ \) There is not enough evidence to reject the claim that chemists in Washington make a different amount than chemists in Florida.
- \( \circ \) There is enough evidence to support the claim that chemists in Washington make a different amount than chemists in Florida.
- \( \circ \) There is not enough evidence to support the claim that chemists in Washington make a different amount than chemists in Florida.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf6690d5-df92-4912-80b3-78d9bef8f763%2F8f2bb095-d528-4958-b16d-4502ee58a979%2F02hgc5_processed.png&w=3840&q=75)
To test
The pooled standard deviation is
Then, the test statistic is
The p-value is 0.
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