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romanna [79]
3 years ago
10

A research paper reports, "… in a sample with 350 observations, the sample average Y = 0.9 is statistically significantly differ

ent from zero at a 5% level, since its t‐statistic is 3.0." Suppose you want to test the null hypothesis that the true mean of the population is equal to one, not zero. Would you reject this null hypothesis (against a two‐sided alternative) at a 5% level?
Mathematics
1 answer:
vladimir2022 [97]3 years ago
8 0

Answer:

I would reject the null hypothesis.

Step-by-step explanation:

The test is a two-tailed test because it is stated that the alternate hypothesis is two-sided.

Degree of freedom = n - 1 = 350 - 1 = 349

At 349 degrees of freedom and 5% significance level, the critical values are -1.96702 and 1.96702

Conclusion:

Reject the null hypothesis because the test statistic 3 falls outside the region bounded by the critical values -1.96702 and 1.96702.

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Marsha wants to determine the vertex of the quadratic function f(x) = x2 – x + 2. What is the function’s vertex?
BaLLatris [955]

Answer:

Vertex = (\frac{1}{2},\frac{7}{4})

Step-by-step explanation:

Given

f(x) = x^2 - x +2

Required

The vertex

We have:

f(x) = x^2 - x +2

First, we express the equation as:

f(x) = a(x - h)^2  +k

Where

Vertex = (h,k)

So, we have:

f(x) = x^2 - x +2

--------------------------------------------

Take the coefficient of x: -1

Divide by 2: (-1/2)

Square: (-1/2)^2

Add and subtract this to the equation

--------------------------------------------

f(x) = x^2 - x +2

f(x) = x^2 - x + (-\frac{1}{2})^2+2  -(-\frac{1}{2})^2

f(x) = x^2 - x + \frac{1}{4}+2  -\frac{1}{4}

Expand

f(x) = x^2 - \frac{1}{2}x- \frac{1}{2}x + \frac{1}{4}+2  -\frac{1}{4}

Factorize

f(x) = x(x - \frac{1}{2})- \frac{1}{2}(x - \frac{1}{2})+2  -\frac{1}{4}

Factor out x - 1/2

f(x) = (x - \frac{1}{2})(x - \frac{1}{2})+2  -\frac{1}{4}

f(x) = (x - \frac{1}{2})^2+2  -\frac{1}{4}

f(x) = (x - \frac{1}{2})^2+ \frac{8 -1 }{4}

f(x) = (x - \frac{1}{2})^2+ \frac{7}{4}

Compare to: f(x) = a(x - h)^2  +k

h = \frac{1}{2}

k = \frac{7}{4}

Hence:

Vertex = (\frac{1}{2},\frac{7}{4})

8 0
3 years ago
Read 2 more answers
Adam wishes to have ​$20 comma 000 available in 18 years to purchase a new car for his son as a gift for his high school graduat
wel

Adam should invest $15516 after 18 years.

<u>Explanation:</u>

Given:

Amount(18) = $20000

Rate of Interest, r = 1.41%

Time, t = 18 years

n = 365 (compounded daily)

General equation of amount that is compounded daily:

A(t) = A_0(1 + \frac{r}{n} )^n^t

Solving for A₀:

A_0 = \frac{A(t)}{(1+\frac{r}{n} )^n^t}

Substituting the values:

A_0 = \frac{20000}{(1 + \frac{0.0141}{365})^3^6^5^X^1^8 } \\\\A_0 = \frac{20000}{1.289}\\ \\A_0 = 15516

Therefore, Adam should invest $15516 after 18 years.

8 0
3 years ago
I need help on how to prove it is a trapezoid - the steps
Vlad1618 [11]
Since all the point connect to prove its a trapezoid, also the fact that it has 1 pair of parallel sides, and to geographic knowledge the sides and angles plus the way it is graphed on the graph it fits the definition of a trapezoid in geographic shapes. Hope this helps lots <3
6 0
3 years ago
An office supply store has five different packages of thumb tacks. Which is the best deal available on thumb tacks at this offic
mezya [45]

Answer:

B

Step-by-step explanation:

We need to find the price of 1 pack for each deal.

12 pack for 2.00

2/12 =$0.17 per pack

24 pack for 3.50

3.50/24 = $0.15 per pack

36 pack for 5.75

5.75/36 = $0.16 per pack

50 pack for 8.25

8.25/50 = $0.17 per pack

100 pack for 15.75

15.75/100 = $0.16 per pack

<em>the lowest deal per pack is for 24 pack for $3.50 since it has the lowest amount per pack.</em>

<em />

<em>correct answer is B</em>

5 0
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The weather report stated that tomorrow's low temperature will be -3 degrees. What does that statement mean?
Firlakuza [10]
It means the temperature will be three degrees below 0.
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3 years ago
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