The true average diameter of ball bearings of a certain type is supposed to be 0.05 in. A one-sample t-test will be carried out to see whether this is the case.
What conclusion is appropriate in each of the following situations?
a. n=13, t=1.6, α=0.05.
b. n=13, t=−1.6, α=0.05.
c. n=25, t=−2.6, α=0.01.

a) H0:

H1:

n = 13 represent the sample size

represent the calculated statistic

The degrees of freedom are given by:

We can calculathe the p value with this formula:

Since we fail to reject the null hypothesis on this case at 5% of significance.

b) H0:

H1:

n = 13 represent the sample size

represent the calculated statistic

The degrees of freedom are given by:

We can calculathe the p value with this formula:

Since we fail to reject the null hypothesis on this case at 5% of significance.

c) H0:

H1:

n = 25 represent the sample size

represent the calculated statistic

The degrees of freedom are given by:

We can calculathe the p value with this formula:

Since we can reject the null hypothesis on this case at 1% of significance.

Step-by-step explanation:

Part a

For this case we assume that we are testing the following system of hypothesis

H0:

H1:

n = 13 represent the sample size

represent the calculated statistic

The degrees of freedom are given by:

We can calculathe the p value with this formula:

Since we fail to reject the null hypothesis on this case at 5% of significance.

Part b

For this case we assume that we are testing the following system of hypothesis

H0:

H1:

n = 13 represent the sample size

represent the calculated statistic

The degrees of freedom are given by:

We can calculathe the p value with this formula:

Since we fail to reject the null hypothesis on this case at 5% of significance.

Part c

For this case we assume that we are testing the following system of hypothesis

H0:

H1:

n = 25 represent the sample size

represent the calculated statistic

The degrees of freedom are given by:

We can calculathe the p value with this formula:

Since we can reject the null hypothesis on this case at 1% of significance.

answer: true

step-by-step explanation:

answer: h

step-by-step explanation: