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snow_tiger [21]
3 years ago
13

3:4 and 4:5 equivalent?

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
8 0

Step-by-step explanation:

As a short answer NO

As a complete answer there's a decimal diference of 0.3333333333

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The net weights (in grams) of a sample of bottles filled by a machine manufactured by Edne, and the net weights of a sample fill
Andru [333]

Answer:

Since is a right tailed test we need to look on the t distribution with 12 degrees of freedom that accumulates 0.05 of the area on the right. And we can use the following excel code:

"=T.INV(0.95,12)" and we got t_{crit}=+1.782

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

\sigma^2_1 =\sigma^2_2 =\sigma^2

And the statistic is given by this formula:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

Where t follows a t distribution with n_1+n_2 -2 degrees of freedom and the pooled variance S^2_p is given by this formula:

\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

This last one is an unbiased estimator of the common variance \sigma^2

The system of hypothesis on this case are:

Null hypothesis: \mu_O \leq  \mu_E

Alternative hypothesis: \mu_O > \mu_E

Or equivalently:

Null hypothesis: \mu_O - \mu_E \leq 0

Alternative hypothesis: \mu_O -\mu_E > 0

Our notation on this case :

n_E =6 represent the sample size for group Edne

n_O =8 represent the sample size for group Orno

\bar X_E =7 represent the sample mean for the group Edne

\bar X_O =10 represent the sample mean for the group Orno

s_E=1.414 represent the sample standard deviation for group Edne

s_O=2.268 represent the sample standard deviation for group Orno

First we can begin finding the pooled variance:

\S^2_p =\frac{(6-1)(1.414)^2 +(8 -1)(2.268)^2}{6 +8 -2}=3.834

And the deviation would be just the square root of the variance:

S_p=1.958

And now we can calculate the statistic:

t=\frac{(10 -7)-(0)}{1.958\sqrt{\frac{1}{6}+\frac{1}{8}}}=2.837

Now we can calculate the degrees of freedom given by:

df=6+8-2=12

Since is a right tailed test we need to look on the t distribution with 12 degrees of freedom that accumulates 0.05 of the area on the right. And we can use the following excel code:

"=T.INV(0.95,12)" and we got t_{crit}=+1.782

Since our calculated value is higher than the critical value we have anough evidence to reject the null hypothesis, and on thsi case the mean for Orno is significanlty higher than the mean for Edne at 5% of significance.

4 0
3 years ago
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