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

The answer is option c.

Answer from: Quest

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

$\frac{ab}{bc} =\frac{ad}{ab}$

now, we can cross multiply

and we get

$ab\timesab=ad\times bc$

$ab^2=ad\times bc$

so, this could be step to prove it

Seth is using the figure shown below to prove pythagorean theorem using triangle similarity: in the

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