What is the simplified expression for 8x + 6 - 14 + 7x

Suppose that you play the game with three different friends separately with the following results: Friend A chose scissors 100 t

Yanka [14]

Answer:

Friend A

$\hat p_A= \frac{100}{400}=0.25$

$z=\frac{0.25 -0.333}{\sqrt{\frac{0.333(1-0.333)}{400}}}\approx -3.47$

Friend B

$\hat p_B= \frac{20}{120}=0.167$

$z=\frac{0.167 -0.333}{\sqrt{\frac{0.333(1-0.333)}{120}}}\approx -3.80$

Friend C

$\hat p_C= \frac{65}{300}=0.217$

$z=\frac{0.217-0.333}{\sqrt{\frac{0.333(1-0.333)}{300}}}\approx -4.17$

So then the best solution for this case would be:

-3.47 (100 out of 400; 25%), -3.80 (20 out of 120; 16.7%), -4.17 (65 out of 300; 21.7%)

Step-by-step explanation:

Data given and notation

n represent the random sample taken

X represent the number of scissors selected for each friend

$\hat p=\frac{X}{n}$ estimated proportion of scissors selected for each friend

$p_o=\frac{1}{3}=0.333$ is the value that we want to test

$\alpha$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion that the friend will pick scissors is less than 1/3 or 0.333, the system of hypothesis would be:

Null hypothesis: $p\geq 0.333$

Alternative hypothesis: $p < 0.333$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .