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3 years ago

Nit Test

Mathematics

1 answer:

bazaltina [42]3 years ago

3 0

Answer:

The graph will be discrete because there is no such thing as a partial person to sign up and the booth is set up once each day for sign ups.

Step-by-step explanation:

The difference between continuous and discrete graphs and functions is that a discrete function allows the variables to be only certain points in the interval, usually only integers; meanwhile, a continuous function allows the variables to be any points in the interval. Here, both variables are discrete, that is, the number of people is {0, 1, 2, 3, ...}, and days are {Monday, Tuesday, Wednesday, ...}

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Answer:

$t=\frac{134.36-135.25}{\sqrt{\frac{15.71^2}{11}+\frac{6.23^2}{8}}}=-0.17$

$p_v =P(t_{(17)}$

So the p value is a very high value and using any significance level for example $\alpha=0,1$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis and we have enough evidence to support the claim. Since the mean for Hylite is not significantly less than the mean for Permafresh.

Step-by-step explanation:

1) Data given and notation

Hylite:[140,139, 138 , 117, 141, 102, 127, 137, 164, 142, 131]

Permafresh:[124,144,136,133,139,132,141,133]

$\bar X_{Hylite}$ represent the mean for the sample Hylite

$\bar X_{permafresh}$ represent the mean for the sample LPermafresh

$s_{Hylite}$ represent the sample standard deviation for the sample Stick

$s_{Permafresh}$ represent the sample standard deviation for the sample Liquid

$n_{Hylite}=11$ sample size for the group Hylite

$n_{Permafresh}=8$ sample size for the group Permafresh

t would represent the statistic (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the mean for Hylite is better for Hylie:

H0: $\mu_{Hylite} \geq \mu_{Permafresh}$

H1: $\mu_{Hylite} < \mu_{Permafresh}$

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{Hylite}-\bar X_{Perm}}{\sqrt{\frac{s^2_{Hylite}}{n_{Hylite}}+\frac{s^2_{Perm.}}{n_{LPerm.}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

In order to calculate the mean and the sample deviation we can use the following formulas:

$\bar X= \sum_{i=1}^n \frac{x_i}{n}$ (2)

$s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}$ (3)

3) Calculate the statistic

First we need to calculate the mean and deviation for each sample, after apply the formulas (2) and (3) we got the following results:

$\bar X_{Hylite}=134.36$ $s_{Hylite}=15.71$

$\bar X_{Permafresh}=135.25$ $s_{Permafresh}=6.23$

And with this we can replace in formula (1) like this:

$t=\frac{134.36-135.25}{\sqrt{\frac{15.71^2}{11}+\frac{6.23^2}{8}}}=-0.17$

4) Statistical decision

For this case we don't have a significance level provided $\alpha$ , but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case: