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mars1129 [50]
3 years ago
10

Hypothesis Testing for Means with Small Samples

Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: volume of root beer in a Windsor Bottling Company can.

A sample of n=24 cans was taken and their contents measured, resulting:

X[bar]= 11.4 oz

S= 0.62 oz

Assuming that the variable has a normal distribution X~N(μ;σ²), the parameter of interest is the average contents of the root beer cans of the Windsor Bottling Company (μ)

The claim is that the population mean content of the cans is different from 12 oz, symbolically: μ ≠ 12

The statistical hypothesis (Null and alternative) have to be complementary, exhaustive and mutually exclusive. The null hypothesis is the "no change" hypothesis and always carries the "=" sign.

If the claim is μ ≠ 12, its complement is μ = 12, the expression carrying the "=" sign will be the null hypothesis and its complement will be the alternative hypothesis:

H₀: μ = 12

H₁: μ ≠ 12

α: 0.05

To test the population mean of this normal population, you have to apply a one sample t-test, with statistic:

t= \frac{X[bar]-Mu}{\frac{S}{\sqrt{n} } } ~t_{n-1}

t_{H_0}= \frac{11.4-12}{\frac{0.62}{\sqrt{24} } } = -4.74

This test is two-tailed, using the critical value approach, you have to determine two rejection regions. Meaning, you'll reject the null hypothesis to small values of the statistic or to high values of the statistic.

t_{n-1;\alpha /2}= t_{23;0.025}= -2.069

t_{n-1;1-\alpha /2}= t_{23;0.975}= 2.069

The decision rule is:

If t_{H_0} ≤ -2.069 or if t_{H_0} ≥ 2.069, then you reject the null hypothesis.

If -2.069 < t_{H_0} < 2.069, then you do not reject the null hypothesis.

The value is less than the left critical value, the decision is to reject the null hypothesis.

Then you can say that with a 5% significance level, there is significant evidence to reject the null hypothesis, then the average amount of root beer of the Windsor Bottling Company is different from 12 oz, this means that the claim about the amount of root beer in the cans is correct.

I hope it helps!

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<u>The difference between the experimental probability and the theoretical probability is 0.08 (rounding the answer to the nearest hundredth) or 8%.</u>

Correct statement and question:

Regina has a bag of 6 orange marbles and 6 black marbles. She picks a marble at random and then puts it back in the bag. She does this 24 times. The results can be found in the table.

Outcome Tally

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Black     14

Figure out the percent error of pulling a black marble in Regina’s experiment. Show your work and round the answer to the nearest hundredth.

Source:

Previous question that can be found at brainly

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Number of orange marbles = 6

Number of black marbles = 6

Number of times of the experiment = 24

Number of times the outcome was an orange marble = 10

Number of times the outcome was a black marble  = 14

2. Figure out the percent error of pulling a black marble in Regina’s experiment. Show your work and round the answer to the nearest hundredth.

The theoretical probability of pulling a black marble is 12/24 or 0.5, given that the number of orange and black marbles are equal and actually, the experimental probability is 14/24 or 0.5833.

We can't describe this difference as an "error". What happened here is that there is a difference between the experimental probability and the theoretical probability.

0.5833 - 0.5 = 0.0833 = 0.08 (rounding the answer to the nearest hundredth)

<u>The difference between the experimental probability and the theoretical probability is 0.08 (rounding the answer to the nearest hundredth) or 8%.</u>

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Step-by-step explanation:

5-3x+x-32

(collect like terms)

5-32-3x+x

<h2><u><em>-27-2x</em></u></h2>
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