11 A random sample of 53 spotted unicorn death certificates from the last decade
ID: 3315713 • Letter: 1
Question
11 A random sample of 53 spotted unicorn death certificates from the last decade has a mean of 443 years with a standard deviation of 132 years. A century ago, mean lifespan for spotted unicorns was 500 years a. What would be the null and alternative hypotheses for a significance test to determine if mean lifespan of spotted unicorns has decreased? b. Do you need to examine the normal plot for this sample before proceeding? If not, why not? c. What type of test would be appropriate for this situation? d. What would be the test statistic for this study? e. What would be the p value? f. What conclusion would you reach? Assume a 0.08 significance level g. If your conclusion is incorrect, what type of error would that be?Explanation / Answer
Sample size n = 53
Sample mean x bar = 443
Sample standard deviation s = 132
Population Mean = 500
.
Part a)
Null hypothesis: Average Lifespan of unicorns is 500
Ho: M = 500
Alternate hypothesis: Average Lifespan of unicorns is less than 500
Ha: M < 500
.
Part b)
The sample size is greater than 30 , thus as per the central limit theorem this sample follows normal distribution
.
Part c)
One sample T test can be done , since the population Standard deviation is unknown
.
Part d)
test statistic
t = (x bar - M) / (s /sqrt(n))
t = (443 -500) / (132 /sqrt(53))
t = -3.1437
.
Part e)
Since it is one tailed test , with df = 53-1 = 52 , and T statistic is -3.1437
The P value would be 0.001378
The formula used in excel to find the P value is =T.DIST.RT(3.1437,52)
.
Part f)
Conclusion: Since p value 0.001378 < alpha 0.08 , we reject the null hypothesis
Thus we conclude that the Mean lifespan is less than 500
.
Part g)
If we end up rejecting the correct null hypothesis this would lead to type I error
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.