Test Statistic
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- Here, the sample size (n) is 150 (extremely large) and population standard deviation (38cm) is known.n=150σ=38
- 1. Based on the report of the school nurse, the average height of Grade 11 students has increased. Five years ago, the average height of Grade 11 students was 170cm with standard deviation of 38cm. She took a random sample of 150 students and derived the average height of 165cm.
- Therefore, the appropriate test statistic to be used is z-test
- 2. It was known that the number of tickets purchased by students at the ticket window for the volleyball match of two popular universities followed a distribution that has mean of 500 and standard deviation of 8.9. Suppose that a few hours before the start of one of these matches, there are 100 eager students standing in line to purchase tickets. If there are 250 tickets remaining, what is the probability that all 100students will be able to purchase the tickets they want?
- Here, the sample size (n) is 100 (extremely large) and population standard deviation (8.9) is known, the instruction only asked to identify what test statistic to be used.n=100; σ=8.9
- Therefore, the appropriate test statistic to be used is z-test
- Here, the sample size (n) is 15 which is less than 30 and sample standard deviation (1.25) was given, while population standard deviation is unknown.n=15s=1.25
- 3. Knowing from a previous study that the average of athletes is 80, an athletic adviser asked how his soccer players are academically doing as compared to other student athletes. After an initiative to help improve the average of student athletes, the adviser randomly selected 15 soccer players and found 85 as the average with standard deviation of 1.25.
- Therefore, the appropriate test statistic to be used is t-test
- Here, the sample size (n) is 20 which is less than 30 and sample standard deviation (40 hours) was given, while population standard deviation is unknown.n=20; s=40
- 4. The CEO of a battery manufacturing company claimed that their batteries would last an average of 280 hours under normal use. A researcher randomly selected 20 batteries from the production line and tested them. The tested batteries had a mean life span of 250 hours with a standard deviation of 40 hours. Do we have enough evidence to suggest that the claim of an average of 280 hours is false?
- Therefore, the appropriate test statistic to be used is t-test
- Variance is the square of the standard deviation and conversely, the standard deviation is the square root of the variance. Hence, if the standard deviation is known in the problem, then basically, variance is also known.
- 5. A study was conducted to look at the average time students exercise. A researcher claimed that in average, students exercise less than 14 hours per month. In a random sample size n=143, it was found that the meantime students exercise is 𝑥̅= 10.3 hours per month with s = 3.43 hours per month.
- Here, the sample size (n) is 143 (extremely large) and sample standard deviation (3.43 hours) was given, while variance is unknown.n=143; s=3.43
- Therefore, the appropriate test statistic to be used is z-test (Central Limit Theorem)
- Now, that is how you can identify the appropriate test statistics involving population mean.
- And that's the end of our lesson for today. See you all in our next class. Thank you and God bless.
- Thank you sir!
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