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Usimov [2.4K]
3 years ago
7

If 7 is the mean of 10,3,4,a,6,9 and 10.find the value of a

Mathematics
1 answer:
nydimaria [60]3 years ago
8 0

Answer:

a = 7

Step-by-step explanation:

I think, what you need to do, is first understand how to find the mean of anything: It's quite simple, actually, just add up all the numbers, then divide that number by the number of numbers. So, let's put it in perspective:

10, 3, 4, a, 6, 9, 10

7 is the mean. 7 is the number of numbers.

If, to find the mean is: 10 + 3 + 4 + a + 6 + 9 + 10= 7a ÷ 7, then: 10 +3 + 4+ 6 + 9 +10= 42

42 plus what divided by 7 is the question now.

42 + a ÷  7= 7

So, 7 times 7, that's 49 minus 42 and you've got your answer: 7

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Answer:

Part A

b. 14.6 ± 7.38

Part B

b. 3.43

Part C

a. P-value < 0.01

Part D

b. There is sufficient evidence to reject the null hypothesis

Step-by-step explanation:

Part A

The given data are;

The number of seedlings in the field = 20

The number of seedlings selected to receive herbicide A = 10

The number of seedlings selected to receive herbicide B = 10

The height in centimeters of seedlings treated with Herbicide A, \overline x _1 = 94.5 cm

The standard deviation, s₁ = 10 cm

The height in centimeters of seedlings treated with Herbicide B, \overline x _2 = 109.1 cm

The standard deviation, s₂ = 9 cm

The 90% confidence interval for μ₂ - μ₁, is given as follows;

\left (\bar{x}_{2}- \bar{x}_{1}  \right )\pm t_{\alpha /2}\sqrt{\dfrac{s_{1}^{2}}{n_{1}}+\dfrac{s_{2}^{2}}{n_{2}}}

The critical-t at 95% and n₁ + n₂ - 2 degrees of freedom is given as follows;

The degrees of freedom, df = n₁ + n₂ - 2 = 10 + 10 - 2 = 18

α = 100% - 90% = 10%

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t_{(0.025, \, 18)} = 1.734

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The 90% C.I. ≈ 14.6 ± 7.38

b. 14.6 ± 7.38

Part B

With the hypotheses are given as follows;

H₀; μ₂ - μ₁ = 0

Hₐ; μ₂ - μ₁ ≠ 0

The two sample t-statistic is given as follows;

t=\dfrac{(\bar{x}_{2}-\bar{x}_{1})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}+\dfrac{s _{2}^{2}}{n_{2}}}}

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The two sample t-statistic ≈ 3.43

b. 3.43

Part C

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Part D

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b. There is sufficient evidence to reject the null hypothesis.

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