1 If there are 47 observations in a sample how many degrees

1. If there are 47 observations in a sample, how many degrees of freedom are there? (The context here is for finding a t value when testing a hypothesis for the population mean).

2. For a given standard error, the larger the difference between two point estimates the greater the p-value for a test of the equality of means. (Hint, try it with two sets of numbers and the same standard error and see which one has the larger p-value then look at it to see if that was a coincidence or if that will always be the case).
a. True

b. False

3. The test statistic for a hypothesis test concerning the value of a population mean when the standard deviation is known and the sample has more than 30 observations follows which distribution?

a. t

b. Z

c. f

d. Chi square

Solution

1.

SInce test is t so degree of freedom is df=n-1=47-1=46.

2.

As the difference between two point estimates increases, value of test statistics increases becuase deifference comes into numerator. As the test statistics incraeses, p-value decreases. So answer : False

3.

It is z-test for single sample becuase population standard deviation is known and sample size is greater than 30.