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3 years ago

How do you solve 28-2.2x=11.6x-54.8??

Mathematics

1 answer:

malfutka [58]3 years ago

6 0

28 - 2.2x = 11.6x - 54.8
28 + 54.8 = 11.6x + 2.2x
82.8 = 13.8x
82.8 / 13.8 = x
6 = x
or x = 6

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Mandarinka [93]

Answer:

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Alternate Hypothesis, $H_A$ : $\mu\neq$ 22 ounces

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Step-by-step explanation:

We are given that a local bottler in Hawaii wishes to ensure that an average of 22 ounces of passion fruit juice is used to fill each bottle.

He takes a random sample of 65 bottles. The mean weight of the passion fruit juice in the sample is 21.54 ounces. Assume that the population standard deviation is 1.38 ounce.

Let $\mu$ = average ounces of passion fruit juice used to fill each bottle.

(a) So, Null Hypothesis, $H_0$ : $\mu$ = 22 ounces {means that the average of 22 ounces of passion fruit juice is used to fill each bottle}

Alternate Hypothesis, $H_A$ : $\mu\neq$ 22 ounces {means that the average different from 22 ounces of passion fruit juice is used to fill each bottle}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean weight of the passion fruit juice = 21.54 ounces

$\sigma$ = population standard deviation = 1.38 ounce

n = sample of bottles = 65

So, test statistics = $\frac{21.54-22}{\frac{1.38}{\sqrt{65} } }$

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Therefore, we conclude that Reject $H_0$ since the value of the test statistic is less than the negative critical value which means that the average different from 22 ounces of passion fruit juice is used to fill each bottle.

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