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Naddika [18.5K]

3 years ago

12

An interior designer purchased 4 1/2 yards, 6 2/3 yards and 9 1/4 yards of fabric to make curtains How many yards of fabric did

they purchase?

2 answers:

Nady [450]3 years ago

6 0

I'm trying to find out the answer

ArbitrLikvidat [17]3 years ago

4 0

Simply add up all.

4 1/2 + 6 2/3 + 9 1/4

(4 + 6 + 9) + 1/2 + 2/3 + 1/4

19 6/12 + 8/12 + 3/12 = (6+8+3)/12 = 17/12

19 17/12

19 1 5/12

19 + 1 5/12

= 20 5/12

20 5/12 yards was purchased.

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Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yi

aalyn [17]

Answer:

a) $t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

$df=12+15-2=25$

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

b) $(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

Step-by-step explanation:

Notation and hypothesis

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 $\sigma^2$

Part a

The system of hypothesis on this case are:

Null hypothesis: $\mu_2 \leq \mu_1$

Alternative hypothesis: $\mu_2 > \mu_1$

Or equivalently:

Null hypothesis: $\mu_2 - \mu_1 \leq 0$

Alternative hypothesis: $\mu_2 -\mu_1 > 0$

Our notation on this case :

$n_1 =12$ represent the sample size for group 1

$n_2 =15$ represent the sample size for group 2

$\bar X_1 =85$ represent the sample mean for the group 1

$\bar X_2 =91$ represent the sample mean for the group 2

$s_1=3$ represent the sample standard deviation for group 1

$s_2=2$ represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

$\S^2_p =\frac{(12-1)(3)^2 +(15 -1)(2)^2}{12 +15 -2}=6.2$

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

$S_p=2.490$

Calculate the statistic

And now we can calculate the statistic:

$t=\frac{(91-85)-(0)}{2.490\sqrt{\frac{1}{12}}+\frac{1}{15}}=6.222$

Now we can calculate the degrees of freedom given by:

$df=12+15-2=25$

Calculate the p value

And now we can calculate the p value using the altenative hypothesis:

$p_v =P(t_{25}>6.222) =8.26x10^{-7}$

Conclusion

So with the p value obtained and using the significance level given $\alpha=0.01$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis.

Part b

For this case the confidence interval is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} S_p \sqrt{\frac{1}{n_1} +\frac{1}{n_2}}$

For the 99% of confidence we have $\alpha=1-0.99 = 0.01$ and $\alpha/2 =0.005$ and the critical value with 25 degrees of freedom on the t distribution is $t_{\alpha/2}= 2.79$

And replacing we got:

$(91-85) -2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =3.309$

$(91-85) +2.79 *2.490 \sqrt{\frac{1}{12} +\frac{1}{15}} =8.691$

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3 years ago

What is the following product in simplified form?

erastova [34]

Answer:

a

Step-by-step explanation:

because I just think its a

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3 years ago

Anthony teaches a pottery painting class in order to save up money for a nice

Marysya12 [62]

Answer:

Anthony teaches a pottery painting class in order to save up money for a nice

bike. In yesterday's class, 5 of the 11 students painted piggy banks.

If Anthony randomly chose 4 of the pieces of pottery to glaze, fire, and set on

the top shelf in a certain order, what is the probability that just the first 2 of the

chosen pieces of pottery are piggy banks?

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3 years ago

Please someone answer my questions please

navik [9.2K]

Answer:

What is your question?

Step-by-step explanation:

8 0

3 years ago

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Graph the line whose x-intercept is -1 and whose y-intercept is 4.<br> x<br> 5<br> ?

shepuryov [24]

Answer:

the x axis is the one that lies flat horizontal this is called the run. the y intercept is the one that goes up and down standing. now you have to plot a dot on the line x moving toward the negative 1 and go up to y meeting up to 4 and that should give you the line to graph

7 0

3 years ago