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Suppose Y is a data matrix, and Z = YF for some orthogonal matrix F, so that Z is a rotated version of Y. Show that the variances of the principal com- ponents are the same for Y and Z. (This result should make intuitive sense.) [Hint: Find the spectral decomposition of the covariance of Z from that of Y, then note that these covariance matrices have the same eigenvalues.]
the time to failure in hours of fans in a personal computer can be modeled by an exponential distribution with
the population proportion is .30. what is the probability that a sample proportion will be within plusmn.04 of the
A researcher looks at the effect of 3 different drugs on 3 different groups of 10 people. Numbers refer to stress levels, with lower numbers being lower stress.
A marketing firm asked a random set of married and single men as to how much they were willing to spend for a vacation. At *alpha*= .05, is a difference in the two amounts?
Generate a 95% confidence interval for the difference in mean HDL levels between men when exercise regularly and those who do not.
If 10% of the parts produced from a manufacturing process are defective, what is the probability that there are 15 or more defectives in a random sample of 100 items?
the following data were collected for a test of linear correlation and spearmans rank correlation was used2.2 3.3 3.3
What is the probability of either X or Y occurring? What is the probability that neither X nor Y will happen?
The standard deviation is 4. what is the best point estimate of the mean? find the 95% confidence interval of the mean score for golfers.
Produce the scatter plot for x3 and y3. Do you think there are any outliers?Calculate the correlation coefficient (r) for all the data points What does the p-value in your SPSS output tell you?
in a survey of top executives it was found that 46 had either traveled internationally on business orcould fluently
a random sample of 121 checking accounts at a bank showed an average daily balance of 280. the population standard
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