It is believed that using a solid state drive (SSD) in a computer results in fas
ID: 3130358 • Letter: I
Question
It is believed that using a solid state drive (SSD) in a computer results in faster boot times when compared to a computer with a traditional hard disk (HDD). You sample a group of computers and use the sample statistics to calculate a 90% confidence interval of (3.43, 10.95). This interval estimates the difference of (average boot time (HDD) - average boot time (SSD)). What can we conclude from this interval?
Question 8 options:
We are 90% confident that the average boot time of all computers with an SSD is greater than the average of all computers with an HDD.
The owner of a local golf course wants to estimate the difference between the average ages of males and females that play on the golf course. He samples a group of men and women and then uses the sample statistics to calculate a 99% confidence interval of (-23.77, -4.44). This interval estimates the difference of (the average age of men - the average age of women). What can we conclude from this interval?
Question 9 options:
The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 26 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 26 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is -1.18 strokes and the standard deviation of the differences is 9.373 strokes. The owner uses this information to calculate the 90% confidence paired t-interval of (-4.32, 1.96). Which statement is the correct interpretation of this interval?
Question 10 options:
1) We are 90% confident that the average boot time of all computers with an HDD is greater than the average of all computers with an SSD. 2) We are 90% confident that the difference between the two sample means falls within the interval. 3) We do not have enough information to make a conclusion. 4) There is no significant difference between the average boot time for a computer with an SSD drive and one with an HDD drive at 90% confidence. 5)We are 90% confident that the average boot time of all computers with an SSD is greater than the average of all computers with an HDD.
The owner of a local golf course wants to estimate the difference between the average ages of males and females that play on the golf course. He samples a group of men and women and then uses the sample statistics to calculate a 99% confidence interval of (-23.77, -4.44). This interval estimates the difference of (the average age of men - the average age of women). What can we conclude from this interval?
Question 9 options:
1) We are 99% confident that the average age of all women who play at the course is greater than the average age of men. 2) We are 99% confident that the average age of all men who play at the course is greater than the average age of all women. 3) We are 99% confident that the difference between the two sample means falls within the interval. 4) There is no significant difference between the average age of men and women that play at the course at 99% confidence. 5) We do not have enough information to make a conclusion.The owner of a golf course wants to determine if his golf course is more difficult than the one his friend owns. He has 26 golfers play a round of 18 holes on his golf course and records their scores. Later that week, he has the same 26 golfers play a round of golf on his friend's course and records their scores again. The average difference in the scores (treated as the scores on his course - the scores on his friend's course) is -1.18 strokes and the standard deviation of the differences is 9.373 strokes. The owner uses this information to calculate the 90% confidence paired t-interval of (-4.32, 1.96). Which statement is the correct interpretation of this interval?
Question 10 options:
1) The proportion of all golfers that had a difference in scores between the two courses is 90%. 2) We are certain the the average difference in scores between the two courses for all golfers is between -4.32 and 1.96. 3) We are 90% confident that the average difference in the scores of the golfers sampled is between -4.32 and 1.96. 4) We are 90% confident that the average difference in scores between the two courses for all golfers is between -4.32 and 1.96. 5) We are 90% confident that the difference between the average score on the owner's golf course and the average score on the friend's golf course is between -4.32 and 1.96.Explanation / Answer
8.
Note that when we do confidence intervals, we do it not just for the sample, but for the whole population.
Hence, as the whole interval is positive, and this is defined as average boot time (HDD) - average boot time (SSD), the HDD times are larger:
OPTION 1: We are 90% confident that the average boot time of all computers with an HDD is greater than the average of all computers with an SSD. [ANSWER]
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9.
Note that when we do confidence intervals, we do it not just for the sample, but for the whole population.
Hence, as the whole interval is negative, and this is defined (the average age of men - the average age of women), the women's ages are larger:
OPTION 1: We are 99% confident that the average age of all women who play at the course is greater than the average age of men. [ANSWER]
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10.
Note that when we do confidence intervals, we do it not just for the sample, but for the whole population.
Hence, as this is a paired difference,
OPTION 4: We are 90% confident that the average difference in scores between the two courses for all golfers is between -4.32 and 1.96.
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