MATHEMATICS COLLEGE

The mean SAT score in mathematics, M, is 600. The standard deviation of these scores is 48. A special preparation course claims that its graduates will score higher, on average, than the mean score 600. A random sample of 70 students completed the course, and their mean SAT score in mathematics was 613. a) At the 0.05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 48.

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

The mean SAT score is $\mu=600$ , we are going to call it \mu since it's the "true" mean

The standard deviation (we are going to call it $\sigma$ ) is

$\sigma=48$

Next they draw a random sample of n=70 students, and they got a mean score (denoted by $\bar x$ ) of $\bar x=613$

The test then boils down to the question if the score of 613 obtained by the students in the sample is statistically bigger that the "true" mean of 600.

- So the Null Hypothesis $H_0:\bar x \geq \mu$

- The alternative would be then the opposite $H_0:\bar x < \mu$

The test statistic for this type of test takes the form

$t=\frac{| \mu -\bar x |} {\sigma/√(n)}$

and this test statistic follows a normal distribution. This last part is quite important because it will tell us where to look for the critical value. The problem ask for a 0.05 significance level. Looking at the normal distribution table, the critical value that leaves .05% in the upper tail is 1.645.

With this we can then replace the values in the test statistic and compare it to the critical value of 1.645.

$t=\frac{| \mu -\bar x |} {\sigma/√(n)}\n\n= (| 600-613 |)/(48/\sqrt(70)}\n\n= (| 13 |)/(48/8.367)\n\n= (| 13 |)/(5.737)\n\n=2.266\n$

since 2.266>1.645 we can reject the null hypothesis.

Answer 2

Answer:

Answer:

The null hypothesis is that the SAT score is not significantly different for the course graduates.

Alternate hypothesis: there is a significant difference between the SAT score achieved by the course graduates as compared to the non-graduates.

Apply the t-test. The Test Statistic value comes out to be t = 1.738 and the p-value = 0.0844

Since the p-value is larger than 0.05, the evidence is weak and we fail to reject eh null hypothesis.

Hope that answers the question, have a great day!

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6x − 2y = 3 (equation 1) 5x + 3y = 4 (equation 2)

Answers

Answer:

there is the answer to do

I need help with # 8 & # 10 please

Answers

Answer:

8) -0.05 lb/day . . . . or . . . . -1.5 lb/month

10) 43.6%

Step-by-step explanation:

8) Using the given units, the "unit rate" is the rate expressed with a denominator of 1. For rates involving time, usually the time period is in the denominator. That is, we're interested in what happens in a unit of time.

... (change in pressure)/(change in time) = (-1.5 lb)/(30 day) = -0.05 lb/day

You can recognize that 30 days is a month, so we could just change the 30 day period to 1 month. Then the denominator will be 1 unit as desired.

... (change in pressure)/(change in time) = (-1.5 lb)/(1 month) = -1.5 lb/month

(My guess is that this latter solution may not fly.)

___

10) 34/78 × 100% = 43.589743_589743% . . . . a repeating decimal with a 6-digit repeat

... ≈ 43.6%

_____

Comment on unit rates involving time

Sometimes, we're interested in the amount of time to do a task. Then the unit rate is expressed as "time per task", rather than "tasks per time".

In the above problem, we might be interested in the amount of time it takes to lose 1 lb of air pressure. Then the unit rate would be 20 days/lb.

Other kinds of unit rates can be inverted similarly, often for similar reasons.

Use any method to multiply (-14ab)(a + 3b - 4c).

Answers

Answer:

-14a^2b-42ab^2+56abc

Step-by-step explanation:

You can use the FOIL method

multiply the first numbers

then inner

then outer

then last

How do you simplify this algebraic expression if a minus sign is in front of the parentheses?

Answers

Treat the negative sign as a -1 and distribute the negative sign to everything inside the parenthesis.

Ex. -(8x^2+3x-1)
-8x^2-3x+1

Basically all the signs flip.

Find the size of angle x.

Answers

Answer:

111°

Step-by-step explanation:

By exterior angle theorem:

$x = 82 \degree + 29 \degree \n = 111 \degree$

Answer:

x = 111

Step-by-step explanation:

180- 82 -29 is 69 and 180-69 is x which x is equal to 111

Need Help What Is -10r+9r

Answers

The value for the expression -10r + 9r is -1r.

what is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

-10r+9r

Now, perform operations to solve

=-10 r + 9r

= r( -10 + 9)

Using properties of integers

(-) x (+ )= -

So,

= r( -1)

= -1r

Learn more about Algebra here:

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