A random sample of 57 chemists from Washington state shows an average salary of $42635, the population standard deviation for chemist salaries in Washington state is $987. A random sample of 35 chemists from Florida state shows an average salary of $49820, the population standard deviation for chemist salaries in Florida state is $789. 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?
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![A random sample of 57 chemists from Washington state shows an average salary of $42,635, with a population standard deviation for chemist salaries in Washington state of $987. In contrast, a random sample of 35 chemists from Florida state shows an average salary of $49,820, with a population standard deviation for chemist salaries in Florida state of $789. A chemist who has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At a significance level of α=0.01, is this chemist correct?
**Let Washington be sample 1 and Florida be sample 2.**
### Hypotheses
- **\( H_0: \mu_1 = \mu_2 \)**
- **\( H_A: \mu_1 \neq \mu_2 \) (claim)**
### Significance Level
Since the level of significance is 0.01, the critical value is 2.576 and -2.576.
### Test Statistic
- **Test statistic:** [ ] (round to 3 places)
### P-value
- **P-value:** [ ] (round to 3 places)
### Decision
The decision can be made to:
- ○ reject \( H_0 \)
- ○ do not reject \( H_0 \)
### Conclusion
- ○ There is enough evidence to reject the claim that chemists in Washington make a different amount than chemists in Florida.
- ○ There is not enough evidence to reject the claim that chemists in Washington make a different amount than chemists in Florida.
- ○ There is enough evidence to support the claim that chemists in Washington make a different amount than chemists in Florida.
- ○ 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%2F635fc7d1-4125-4a99-970f-fc3f5300d520%2F03cde4b5-fd00-4f28-a325-1bb52eab4d82%2Fbjyo1v2_processed.png&w=3840&q=75)
Let denotes the population mean salary for Washington state, and denotes the population mean salary for Florida state.
The claim of the test is that the chemists in Washington make a different amount than chemists in Florida. The hypothesis is,
Null hypothesis:
Alternative hypothesis:
Correct Answer: Option 3.
The sample size of Washington state is 57 with average salary $42,635, the population standard deviation is $987, sample size of Florida state us 35 with average salary $49,820, the population standard deviation is $789.
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