What is the critical value for t for a two-tailed test with 9 degrees of freedom

Question

What is the critical value for t for a two-tailed test with 9 degrees of freedom and = 0.10?

Question 1 options:

1.83

1.38

2.26

1.86

Question 2 (0.5 points)

For a two-tailed test, what proportion of your alpha () would be allotted to the highest tail of the distribution if you have a total = 0.10?

Question 2 options:

Cannot be determined with the given information

0.10

0.025

0.05

Question 3 (0.5 points)

For a two-tailed test, the researcher is examining which proportion(s) of the distribution?

Question 3 options:

Highest proportion

Either the highest or the lowest proportion

Lowest proportion

Both the highest and lowest proportions

Question 4 (0.5 points)

If a sample has n = 100, how many degrees of freedom with the one sample t-test have?

Question 4 options:

100

99

101

Cannot be determined with the given information

Question 5 (0.5 points)

Which of the following terms is not required when calculating the t statistic?

Question 5 options:

SD

n

M

Question 6 (0.5 points)

A single sample t-test is used _____.

Question 6 options:

to compare a sample mean to a known population mean

to compare a sample mean to a different sample's mean

All other answers are incorrect.

to compare two means from the same sample

Question 7 (0.5 points)

The null hypothesis for a two-tailed, single (one) sample t-test states that _____.

Question 7 options:

there is no difference between the sample mean and the population mean

the sample mean is greater than the population mean

the sample mean is less than the population mean

the sample mean is different from the population mean

Question 8 (0.5 points)

For a one-tailed test, the researcher is examining which proportion(s) of the distribution?

Question 8 options:

Highest proportion

Lowest proportion

Either the highest or the lowest proportion

Both the highest and lowest proportions

Question 9 (0.5 points)

In which of the following situations is it NOT appropriate for a researcher to choose to use a one-tailed test instead of a two-tailed test?

Question 9 options:

The researcher is only interested in whether the sample mean is significantly lower than the population mean.

The researcher did not find a significant result with a two tailed test.

All three are reasons that a researcher should use a one-tailed test.

The researcher is only interested in whether or not the sample mean is significantly higher than its population mean.

Question 10 (0.5 points)

A sample with a size of 100 has a mean of 40 and a standard deviation of 5. What would the t-value for the sample be if it were compared to a population mean of 46?

Question 10 options:

t = 12.00

t = -12.00

t = -120.00

t = -1.20

1.83

1.38

2.26

1.86

Explanation / Answer

Question 1:

For a two tailed t -test, and for 9 degrees of freedom, we get from the t-distribution tables that:

P( t9 < 1.833 ) = 0.95 and therefore due to symmetry, we get:

P( -1.833 < t9 < 1.833 ) = 0.9

Therefore 1.833 is the required critical value here.

Question 2:

For a two tailed test, both the tails are given equal amount of area. Therefore the level of significance of 0.1 would be equally divided as 0.05 in each of the two tails.

Therefore 0.05 is the correct answer here.

Question 3:

For a two tailed test, the researching is obviously looking from both sides and therefore is examining both the tails.

Question 4:

For a sample size of n = 100, one sample t test would be done at n-1 = 99 degrees of freedom

Therefore 99 degrees of freedom is the correct answer here.

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