Is the ordered pair given a solution to the equation.

When I sit and watch my students take exams, I often think to myself "I wonder if students with bright calculators are impacted

hodyreva [135]

Answer:

There is a difference between the two means.

Step-by-step explanation:

The hypothesis can be defined as:

H₀: The mean exam scores of my SAT 215 students with colorful calculators are same as the mean scores of my STA 215 students with plain black calculators, i.e. μ₁ - μ₂ = 0.

Hₐ: The mean exam scores of my SAT 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators, i.e. μ₁ - μ₂ ≠ 0.

Assume that the significance level of the test is, α = 0.05. Also assuming that the population variances are equal.

The decision rule:

A 95% confidence interval for mean difference can be used to determine the result of the hypothesis test. If the 95% confidence interval contains the null hypothesis value, i.e. 0 then the null hypothesis will not be rejected.

The 95% confidence interval for mean difference is:

$CI=\bar x_{1}-\bar x_{2}\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\times S_{p}\times \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}$

Compute the pooled standard deviation as follows:

$S_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}} {n_{1}+n_{2}-2}}}=\sqrt{\frac{(49-1)(4.7)^{2}+(38-1)(5.7)^{2}}{49+38-2}}=5.16$

The critical value of t is:

$t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (49+38-2)}=t_{0.025, 85}=1.984$

*Use a t-table.

Compute the 95% confidence interval for mean difference as follows:

$CI=\bar x_{1}-\bar x_{2}\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\times S_{p}\times \sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}$

$=(84-87)\pm 1.984\times 5.16\times \sqrt{\frac{1}{49}+\frac{1}{38}}$

$=-3\pm 2.133\\=(-5.133, -0.867)\\\approx(-5.13, -0.87)$

The 95% confidence interval for mean difference is (-5.13, -0.87).

The confidence interval does not contains the value 0. This implies that the null hypothesis will be rejected at 5% level of significance.

Hence, concluding that the mean exam scores of my STA 215 students with colorful calculators are different than the mean scores of my STA 215 students with plain black calculators.

7 0

4 years ago

Un cultivo de bacterias se duplica cada hora. Si inicialmente, hay 1 bacteria, determina el numero de bacterias que se obtienen

guapka [62]

Answer:

Hour 3

4 * 2 = 8

Hour 4

8 * 2 = 16

Hour 6

32 * 2 = 64

Hour 7

64 * 2 = 128

Hour 12

2048 * 2 = 4096

Step-by-step explanation:

We are told that initially there is a bacterium that doubles every hour, so let's calculate what happens in the first 12 hours every hour.

Hour 0

one

Hour 1

1 * 2 = 2

Hour 2

2 * 2 = 4

Hour 3

4 * 2 = 8

Hour 4

8 * 2 = 16

Hour 5

16 * 2 = 32

Hour 6

32 * 2 = 64

Hour 7

64 * 2 = 128

Hour 8

128 * 2 = 256

Hour 9

256 * 2 = 512

Hour 10

512 * 2 = 1024

Hour 11

1024 * 2 = 2048

Hour 12

2048 * 2 = 4096

We can deduce that the growth of the bacteria is:

2 ^ n

where n is the # of time that has passed

6 0

4 years ago

How many solutions does the equation 2p + 9 = 5 + 4 + 2p have?

spayn [35]

Answer:

infinite solution

Step-by-step explanation:

the y intercept and the slope are the same

8 0

3 years ago

$29000; 4 percent decrease

yulyashka [42]

The easiest way to calculate this, since you don't need to know what the discount is, if the decrease is 4% you still have 96%. Multiply 29,000 x .96= $27,840. If you do it the other way, .04 x 29000= 1160. Then subtract 29000-1160=27850.

6 0

3 years ago

Which brand of rice is the better buy? Explain your reasoning.

Ad libitum [116K]

So you have to divide the amount by how many you’re buying and get the unit rate per each ounce so the answer is b

5 0

3 years ago

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