Choose the function

A random sample of 35 undergraduate students who completed two years of college were asked to take a basic mathematics test. The

lisov135 [29]

Answer:

$(75.1 -72.1) -1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= -1.96$

$(75.1 -72.1) +1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= 7.96$

And the confidence interval would be given by:

$-1.96 \leq \mu_1 -\mu_2 \leq 7.96$

And since the confidence interval contains the value 0 we have enough evidence to conclude that we don't have significant differences between the two means at 10% of significance.

Step-by-step explanation:

For this case we have the following info given :

$\bar X_1= 75.1$ represent the sample mean for the scores of the undergraduate students

$s_1 = 12.8$ represent the standard deviation for the undergraduate students

$n_1 =35$ the sample size for the undergraduate

$\bar X_2= 72.1$ represent the sample mean for the scores of the high school students

$s_2 = 14.6$ represent the standard deviation for the high school students

$n_2 =50$ the sample size for the high school

The confidence interval for the true difference of means is given by:

$(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}$

The degrees of freedom are given by:

$df=n_1 +n_2 -2= 35+50-2=83$

The confidence level is 90% and the significance level is $\alpha=0.1$ and $\alpha/2 =0.05$ then the critical value would be:

$t_{\alpha/2}= 1.99$

And replacing the info we got:

$(75.1 -72.1) -1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= -1.96$

$(75.1 -72.1) +1.66 \sqrt{\frac{12.8^2}{35} +\frac{14.6^2}{50}}= 7.96$

And the confidence interval would be given by:

$-1.96 \leq \mu_1 -\mu_2 \leq 7.96$

And since the confidence interval contains the value 0 we have enough evidence to conclude that we don't have significant differences between the two means at 10% of significance.

8 0

2 years ago

The price of your service plan before taxes is 89.99. For your convenience, I will deduct 15% off your service plan before taxes

Citrus2011 [14]

First, you must find how much $ the discount takes off
89.99 * .15
=13.4985

Subtract that from 89.99

=76.4915

If you estimate it,
$ 76.49

5 0

2 years ago

To solve -9 - 16m = 7, what steps would you use?

Ne4ueva [31]

First your going to add 9 to both sides.

-9-16m=7 ---> 16m=16

then you just divide them. so m should equal 1

7 0

2 years ago

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of

nydimaria [60]

This question is incomplete. I got the complete part (the boldened part) of it from google as:

The following 98% confidence interval was obtained for μ1 - μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B:

4.90 hrs < μ1 - μ2 < 17.50 hrs.

Answer:

A paint manufacturer made a modification to a paint to speed up its drying time. Independent simple random samples of 11 cans of type A (the original paint) and 9 cans of type B (the modified paint) were selected and applied to similar surfaces. The drying times, in hours, were recorded. The summary statistics are as follows. Type A Type B x 1x1equals=76.3 hr x 2x2equals=65.1 hr s 1s1equals=4.5 hr s 2s2equals=5.1 hr n 1n1equals=11 n 2n2equals=9 The following 98% confidence interval was obtained for mu 1μ1minus−mu 2μ2, the difference between the mean drying time for paint cans of type A and the mean drying time for paint cans of type B. What does the confidence interval suggest about the population means?

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Step-by-step explanation:

The mean difference for the 98% confidence interval, the drying times of the two types of paints are (4.90, 17.50). This implies that Type A paint takes between 4.90 and 17.50 hours more to dry than type B paint.

Only positive values comprise the confidence interval which suggests that the mean drying time for paint type A is greater than the mean drying time for paint type B. The modification appears to be effective in reducing drying times.

7 0

2 years ago

8. Derek was observing the change in water levels in his fish pond. The table below show the change in water levels of the fish

Alla [95]

Answer:

H. 2 3/4

Step-by-step explanation:

DATE >> WATER LEVEL CHANGE (inches)
August 25 >> -0.75
September 8 >> -1 3/ 8
September 22 >> 2.5
October 6 >> -1/2
October 20 >> 1 7/8

<u>Total change:</u>

1 7/8 - (-0.75) =
1+ 7/8 + 3/4 =
1 + 7/8 + 6/8 =
1 + 13/8 =
1+ 1 5/8 =
2 5/8

The closest answer option is H. 2 3/4

8 0

2 years ago