Mathematics, 02.03.2020 17:32 bgallman153p71edg

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.

Answers: 3

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Answer from: sandra5456

a) H0: $\mu \leq \mu_o$

H1: $\mu \mu_o$

n = 13 represent the sample size

t = 1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

$p_v = P(t_{12} 1.6) = 0.068$

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

b) H0: $\mu \geq \mu_o$

H1: $\mu < \mu_o$

n = 13 represent the sample size

t = -1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

$p_v = P(t_{12}$

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

c) H0: $\mu \geq \mu_o$

H1: $\mu < \mu_o$

n = 25 represent the sample size

t = -2.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 25-1=24

We can calculathe the p value with this formula:

$p_v = P(t_{24}$

Since p_v 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: $\mu \leq \mu_o$

H1: $\mu \mu_o$

n = 13 represent the sample size

t = 1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

$p_v = P(t_{12} 1.6) = 0.068$

Since $p_v \alpha$ 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: $\mu \geq \mu_o$

H1: $\mu < \mu_o$

n = 13 represent the sample size

t = -1.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 13-1=12

We can calculathe the p value with this formula:

$p_v = P(t_{12}$

Since $p_v \alpha$ 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: $\mu \geq \mu_o$

H1: $\mu < \mu_o$

n = 25 represent the sample size

t = -2.6 represent the calculated statistic

The degrees of freedom are given by:

df = n-1 = 25-1=24

We can calculathe the p value with this formula:

$p_v = P(t_{24}$

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

Answer from: Quest

u what ?

step-by-step explanation:

Answer from: Quest

Ihope this and i’m only writing this because my thing has to be longer

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