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3 years ago

This equation needs to be solved

Mathematics

2 answers:

ella [17]3 years ago

6 0

-28n - 4 + 2n - 8 = 66

-26n - 12 = 66

-26n = 78

n = -3

velikii [3]3 years ago

3 0

66 = -4(7n + 1) + 2(n - 4)

Distribute -4 inside the parentheses.

66 = -28n - 4 + 2(n - 4)

Distribute 2 inside the parentheses.

66 = -28n - 4 + 2n - 8

Combine like terms.

66 = -26n - 12

Add 12 to both sides.

78 = -26n

Divide both sides by -26.

n = -3

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Answer:

Step-by-step explanation:

From the given information:

Let:

$\mu_1$ represent the population mean no. for DH group.

$\mu_2$ represent the population mean no. for no DH group

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$n_2$ represent the sample sizes of no DH

Sample size: $n_1 = n_2 = 20$

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The null & alternative hypothesis;

$H_o : \mu_1 \le \mu_2 \\ \\ H_a: \mu_1 > \mu_2$

Level of significance:

The test statistics is:

$z = \dfrac{\bar x_1 - \bar x_2}{\sqrt{\dfrac{\sigma^2_1}{n_1} + \dfrac{\sigma_2^2}{n_2} }}$

where;

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$\implies \dfrac{1}{n_1} \sum \limit ^{n_1}_{i=1} x_1 \\ \\ = \dfrac{1}{20}(0+6+8+2+2+4+7+7+6+5+1+1+5+4+4+5+7+11+10+0) \\ \\ = \dfrac{92}{20}$

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Now:

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Since the test is one-tailed by looking at that $H_a:$

The P-value = $P(Z > z)$

$\implies 1 - P(Z \le z) \\ \\ = 1 - P(Z \le 0.5602)$

Using Excel Function " =normdist(z)"; we have":

$= 1- 0.7123$

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Decision rule: To reject $H_o$ , if $p-value < \alpha \ at \ 0.10$

Conclusion: SInce P = 0.2877 which is $> \ \alpha \ at \ 0.10.$

We fail to reject the $H_o$ and conclude that there is insufficient evidence to support the given claim that: $\text{more runs are scored in games for which DH is used.}$

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