Please explain, I will give you a good rating if you do it right 1) Investigator
ID: 3268518 • Letter: P
Question
Please explain, I will give you a good rating if you do it right
1)
Investigators want to test whether people who worked overnight shifts reported less sleep per day than the general population. They conduct a one-tailed, one-sample t-test, comparing the mean number of hours of sleep in a sample of people who worked overnight shifts (sample mean= 6.5 hours) to the general population mean of 7.5 hours. Their calculated t-statistic had a corresponding p-value of 0.0345. Which of the following represents the best interpretation of this p-value?
The probability of obtaining a result less extreme than the one observed if the null hypothesis was true is 3.45%.
2)
A population of low birth weight infants is found to have a mean (µ) weight of 5 pounds with a standard deviation () of 0.5 pounds. It is determined that approximately 80% of this population of infants falls between a z-score of +1.28 and –1.28. Another way of interpreting this information about this population of infants is:
Approximately 80% of infants fall within 1.28 standard deviations above and below the mean.
3)
When comparing a single sample to a population mean, a one-sample t-test must be used instead of a one-sample z-test when what value is unknown?
- 3.45% of people who worked overnight shifts reported more than 7.5 hours of sleep per day.Explanation / Answer
1. The p value refer to probability of observing a test statistic as large as the one computed, assuming null hypothesis to be true. The main point in interpreting the p value is understanding the null hypothesis, which is the hypothesis of no difference. Thus, assuming that there is no difference between the mean hours of sleep for people who worked overnight and general population, the probability of obtaining the result from test as large as the one computed is 0.0345. Going by th elogic, the options 1, 2, 4 and 5 are cancelled out. Thus, correct answer is option 3.
2. The Z score tells that how many standard deviations an element is from the mean. Thus, from given information 80% of population infants fall within z=1.28 and z=-1.28. This can best be interpreted by option 5. Option 1 and 2 have wrong units, option 3 has wrong value, option 4 has wrong value and wrong interpretation.
3. For computing a one sample t test, using following formula
t=(xbar-mu)/(s/sqrt n), where, xbar is sample mean, mu is population mean, s is sample standard deviation, n is sample size.
One need to know sample mean, sample stanadard deviation, alpha level to compute p value of test statistic or critical t.
The t test is performed instead of z test, when the population standard deviation, sigma is unknown. Option 2 is correct. The options 1, 3, 4 and 5 are discarded.