a) What is the p value for this test? b) Would the null value have been rejected if this was a 1% level test? YN c) Would the null value have been rejected if this was a 0.1% level test? YN d) What was the value of x calculated from our sample?
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!
Suppose we are testing the null hypothesis H0: ? = 13 against the alternative Ha: ? > 13 from a normal population with known standard deviation ?=5. A sample of size 256 is taken. We use the usual z statistic as our test statistic. Using the sample, a z value of 2.636 is calculated. (Remember z has a standard
a) What is the p value for this test?
b) Would the null value have been rejected if this was a 1% level test?
c) Would the null value have been rejected if this was a 0.1% level test?
d) What was the value of x calculated from our sample?
a)
The hypothesis is right tail. The p-value for right tailed test is,
The probability of z less than 2.636 can be obtained using the excel formula “=NORM.S.DIST(2.636,TRUE)”. The probability value is 0.9958.
The required p-value is,
Thus, the p-value for this test is 0.0042.
b)
Decision rule:
If p-value, then reject the null hypothesis. Otherwise, do not reject the null hypothesis.
Conclusion:
The p-value (0.0042) is less than the level of significance (0.01).
Based on the decision rule, reject the null hypothesis.
Yes, the value have been rejected if this was a 1% level test.
c)
Conclusion:
The p-value (0.0042) is greater than the level of significance (0.001).
Based on the decision rule, do not reject the null hypothesis.
No, the value have been not rejected if this was a 0.1% level test.
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