You wish to test the following claim (H.) at a significance level of a = 0.02. H¸:µ = 62.8 Ha:µ # 62.8 You believe the population is normally distributed and you know the standard deviation is o = 13.4. You obtain a sample mean of M = 61 for a sample of size n = 44.
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!
![You wish to test the following claim (\(H_a\)) at a significance level of \(\alpha = 0.02\).
\[
H_o: \mu = 62.8
\]
\[
H_a: \mu \neq 62.8
\]
You believe the population is normally distributed and you know the standard deviation is \(\sigma = 13.4\). You obtain a sample mean of \(M = 61\) for a sample of size \(n = 44\).
What is the test statistic for this sample? (Report answer accurate to three decimal places.)
\[ \text{test statistic} = \_\_\_ \]
What is the p-value for this sample? (Report answer accurate to four decimal places.)
\[ \text{p-value} = \_\_\_ \]
The p-value is...
- [ ] less than (or equal to) \(\alpha\)
- [ ] greater than \(\alpha\)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe99d77bd-6783-440b-95ab-8e6a48270523%2F262b2a7f-0ac6-40c0-a168-393eada4c6b5%2Fpc2lsvw_processed.jpeg&w=3840&q=75)
The test statistic is,
Thus, the test statistic is -0.891.
The hypothesis is two tail. The p-value for two tailed test is,
The probability of z less than –0.891 can be obtained using the excel formula “=NORM.S.DIST(–0.891,TRUE)”. The probability value is 0.18647.
The required P-value is,
Thus, the p-value is 0.3729.
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