求 X 的樣本變異數,Y 的樣本變異數以及 X , Y 的樣本共變異數。
考慮以 X 預測Y 簡單迴歸模式,Y =α +βX ,則β 的最小平方估計值為何?
截距α 項的估計值為何?
請寫出p 的估計值的近似分配。
請問檢定p 值為何?
如果真正的報考率為31%,則在5%的顯著水準下,此檢定的檢定力為何?
瓦斯行公會自治公約規定,20 公斤裝的瓦斯瓶,容許0.5 公斤的誤差。某瓦斯配
銷點以機器裝填瓦斯,假設瓦斯裝填量呈常態分配,設定的平均值為m 公斤,標
準差為0.2 公斤。
為使符合自治公約的瓦斯瓶比例達到95%以上,請問m 應該設為多少?
瓦斯行公會自治公約規定,20 公斤裝的瓦斯瓶,容許0.5 公斤的誤差。某瓦斯配
銷點以機器裝填瓦斯,假設瓦斯裝填量呈常態分配,設定的平均值為m 公斤,標
準差為0.2 公斤。
Suppose that an run contain 1 10 N = blue balls and 2 10 N = red balls. Let X
denote the number of blue balls in a random sample of size n =15 .
Suppose the sampling is done one at a time without replacement. Find P[X = 6] .
0.005
0.092
0.246
0.153
Suppose that an run contain 1 10 N = blue balls and 2 10 N = red balls. Let X
denote the number of blue balls in a random sample of size n =15 .
Suppose the sampling is done one at a time with replacement. Find P[X = 6] .
0.005
0.153
0.205
0.304
Suppose that an run contain 1 10 N = blue balls and 2 10 N = red balls. Let X
denote the number of blue balls in a random sample of size n =15 .
Which of the following statement is false?
The expected numbers of blue balls from these two sampling methods are equal.
The variances of X from these two sampling methods are equal.
When the sampling is done with replacement, Var(X ) = 3.75 .
Determine which of the following measure can be used to measure the variation
Interquartile range
Mean
Mode
Medium.
Determine which of the following statistical graph is most appropriate to summary the
exam scores ranged as A , B , C , D , F .
Box plot
Pie chart
Stem-and-leaf diagram
Histogram.
Which of the following summary measure has least influence, when data include
outliers?
Mean
Medium
Range
Variance.
Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars
accounted for 18% of the vehicles on the road, but accident involving small cars led to
11898 fatalities during a recent year. Assume the probability a small car is involved in
an accident is 0.18. The probability of an accident involving a small car leading to a
fatality is 0.128 and the probability of an accident not involving a small car leading to a
fatality is 0.05. Suppose you learn of an accident involving a fatality. What is the
probability a small car was involved?
0.023
0.041
0.128
0.360.
During the period of time that a local university takes phone-in registrations, calls
come in at the rate of one every two minute.
What is the expected number of calls in two hour?
1
30
60
120
During the period of time that a local university takes phone-in registrations, calls
come in at the rate of one every two minute.
What is the probability of three calls in six minute?
0.125
0.224
0.647
0.934
Given that the population has a normal distribution, derive a 95% confidence
interval for the population mean number of hours of sleep each night.
(6.56, 6.86)
(6.56, 7.16)
(6.54, 7.18)
(5.26, 8.46)
Suppose the investigator would like to construct a 95% confidence interval with the
desired margin of error being 0.1. Based on the information obtained from given
sample, how many individuals should be included in the sample.
223
233
248
258
In the game of craps, a player rolls two unfaired four-sided dice. Suppose we can
observe the upper-faced side of die. Assume the probability of getting the odd number
is 1/6 and the probability of getting the even number is 1/3. There are 16 possible
outcomes.
Determine the probability of the event that the sum of dice is 3.
1/16
1/9
1/4
2/16
In the game of craps, a player rolls two unfaired four-sided dice. Suppose we can
observe the upper-faced side of die. Assume the probability of getting the odd number
is 1/6 and the probability of getting the even number is 1/3. There are 16 possible
outcomes.
Determine the probability of the event that the sum of dice is either 2 or 7.
2/16
3/16
5/36
8/36
Microsoft Outlook is the most widely used e-mail manager. A Microsoft executive
claims that Microsoft Outlook is used by at least 75% of Internet users. A sample of
Internet users will be used to test this claim.
A Merrill Lynch study reported that Microsoft Outlook is used by 72% of Internet
users. Assume that the report was based on a sample size of 300 Internet users. Let
the test value be denoted as T and the corresponding p -value be denoted as P .
Find (T, P) .
(−1.2, 0.1151)
(−1.2, 0.8849)
(1.2, 0.1151)
(1.2, 0.8849)
Microsoft Outlook is the most widely used e-mail manager. A Microsoft executive
claims that Microsoft Outlook is used by at least 75% of Internet users. A sample of
Internet users will be used to test this claim.
Given a significance level of 0.05, find the power of the test when you suspect the
true proportion is 78%.
0.206
0.319
0.681
0.794
Microsoft Outlook is the most widely used e-mail manager. A Microsoft executive
claims that Microsoft Outlook is used by at least 75% of Internet users. A sample of
Internet users will be used to test this claim.
Suppose you do not have any idea about the proportion of Internet users using
Microsoft Outlook. Assume the confidence level of 0.95. How large a sample
should be taken if you want to construct a confidence interval with a margin of
error being 0.05?
204
263
289
385
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