Exam 10: A: Inference From Small Samples

The t distribution with n - 1 degrees of freedom is used when testing a null hypothesis for a population variance.

In testing vs. the larger sample variance must be used as the numerator of the F test statistic.

In comparing two population means of interval data, we must decide whether the samples are independent (in which case the parameter of interest is ) or matched pairs (in which case the parameter is ) in order to select the correct test statistic.

For to have an F distribution, random samples must be drawn from each of two normal populations and be independent.

As the degrees of freedom for the t distribution increase, which of the following distributions does it more and more closely approximate?

If you wish to test vs. at the 0.05 level of significance using a sample of 20 observations, the critical values to be used are 32.852.

The 5th percentile of a chi-square distribution with 10 degrees of freedom is equal to 4.3903.

In testing the difference between the means of two normally distributed populations, the number of degrees of freedom associated with the unequal-variances t test statistic usually results in a non-integer number. In this situation, what is the best recommendation in order to proceed?

In a hypothesis test for a population variance , the critical value increases as the sample size increases for a given level of significance.

If you were constructing a 99% confidence interval for the population mean based on a sample of n = 25, where the standard deviation of the sample s = 0.05, what would be the critical value of t?

The Student's t distribution has more area in the tails and less in the centre than does the normal distribution.

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in Canada revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield = 180.975 and s = 143.042. Which of the following is a 95% confidence interval for the mean endowment of all the private colleges in Canada?

In testing vs. you are free to decide which of the two populations you want to call "Population 1."

The quantity is called the pooled variance estimate of the common variance of two unknown but equal population variances. It is the weighted average of the two sample variances. What do the weights represent?

The pooled-variances t-test requires that the two population variances need not be the same.

A hypothesis test is to be conducted regarding a population variance. Which distribution would be used to obtain the critical value of the test?

Which of the following statements is correct regarding the percentile points of the F distribution? A) B) C) D)

A random sample of size 25 taken from a normally distributed population resulted in a sample standard deviation of 0.93054. What are the lower and upper limits of a 99% confidence interval for the population variance?

The chi-square critical value denotes the number on the measurement axis such that 10% of the area under the chi-square curve with 6 degrees of freedom lies to the right of .

Statisticians have shown that the mathematical process that derived the Student's t distribution is robust, which means that if the sampled population is non-normal, the t test of the population mean is still valid, provided that the population is not extremely non-normal.