In a test of Ho: H= 90 against Ha:u> 90, the sample data yielded the test statistic z = 2.17. Find and interpret the p-Value for the test. E Click the icon to view a table of standard normal values The p-value is p= 0.015 (Round to three decimal places as needed.) Interpret the results. What does this p-value mean? O A. The probability of observing a z-value<2.17 is equal to the p-value, if u> 90. O B. The probability of observing a z-value> 2.17 is equal to the p-value, if u > 90. O C. The probability of observing a z-value> 2.17 is equal to the p-value, if u = 90. O D. The probability of observing a z-value<2.17 is equal to the p-value, if u = 90.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
![### Hypothesis Testing Example
In a test of \( H_0: \mu = 90 \) against \( H_a: \mu > 90 \), the sample data yielded the test statistic \( z = 2.17 \). Find and interpret the p-value for the test.
#### Instructions:
Click the icon to view a table of standard normal values.
#### Calculation of p-value:
The p-value is \( p = 0.015 \).
(Round to three decimal places as needed.)
### Interpretation of Results:
What does this p-value mean?
#### Options:
- **A.** The probability of observing a z-value \( < 2.17 \) is equal to the p-value, if \( \mu = 90 \).
- **B.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu > 90 \).
- **C.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu = 90 \).
- **D.** The probability of observing a z-value \( < 2.17 \) is equal to the p-value, if \( \mu > 90 \).
#### Correct Answer:
- **C.** The probability of observing a z-value \( > 2.17 \) is equal to the p-value, if \( \mu = 90 \).
This means that there is a 1.5% chance of observing a test statistic as extreme as 2.17 or more extreme in the direction of the alternative hypothesis, assuming the null hypothesis is true.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d0fca7b-87e2-42be-9458-260269753889%2F570d32d6-014d-46b7-a132-af33af43e2fc%2Fc66bsrj_processed.jpeg&w=3840&q=75)
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