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Paraphin [41]
2 years ago
7

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation

is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null hypothesis? Question 50 options: 16.2 ounces 16.041 ounces 15.8 ounces 16.049 ounces
Mathematics
1 answer:
S_A_V [24]2 years ago
3 0

Answer:

The correct option is 16.041 ounces.

Step-by-step explanation:

A single mean test can be used to determine whether the average amount of shampoo per bottle is 16 ounces.

The hypothesis can be defined as:

<em>H₀</em>: The average amount of shampoo per bottle is 16 ounces, i.e. <em>μ</em> = 16.

<em>Hₐ</em>: The average amount of shampoo per bottle is different from 16 ounces, i.e. <em>μ</em> ≠ 16.

The information provided is:

n=64\\\sigma=0.20\\\alpha =0.10

We can compute a 90% confidence interval to determine whether the population mean is 16 ounces or not.

Since the population standard deviation is known we will compute the <em>z-</em>interval.

The critical value of <em>z</em> for 90% confidence interval is:

z_{0.05}=1.645

*Use a <em>z-</em>table.

Compute the 90% confidence interval for population mean as follows:

CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\

Since the sample size is quite large, according to the law of large numbers the on increasing the sample size, the mean of the sample approaches the whole population mean.

So, the 90% confidence interval estimate for sample mean is:

CI=\mu\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\=16\pm 1.645\times \frac{0.20}{\sqrt{64}}\\=16\pm0.041125\\=(15.958875, 16.041125)\\\approx (15.959, 16.041)

Thus, the correct option is 16.041 ounces.

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Answer:

<u>The correct answer is B. 1/729</u>

Step-by-step explanation:

1. Probability of any of the nine words would be randomly cited.

Using the Laplace Rule, we calculate that probability is 1/9

2. Now let's calculate the probability of any two - word phrase in specific order from those nine in the dictionary. We should remember that the probability of occurrence of two or more statistically independent events is equal to the product of their individual probabilities. So,

1/9 * 1/9 = 1/81

3. Using the same Multiplication Rule, we can calculate the probability of a random generation of the phrase "three blind mice", in that specific order. Because there are other phrases that could be generated with those three words, but in different order.  The question was specific about the order.

1/9 * 1/9 * 1/9 = 1/729

<u>The probability of randomly generating the phrase "three blind mice" is 1/729 or 0.137%</u>

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3 years ago
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Answer:

Step-by-step explanation:

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2x - 8 = -10

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2 years ago
What is 84 seconds to 8 seconds
Inessa05 [86]

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200 out of 238: 16% decrease

Step-by-step explanation:

To find a percent decrease, you first subtract the end number by the initial number. This gives you the change.

ex. 84-8=76

Now you divide the change by the initial number. You'll get a decimal.

ex. 76/84=0.904...

Multiply the decimal times 100, or move the decimal to the right twice.

ex. 0.904... -> 90.4...

Now round to the nearest ones place

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8/9+ (-5/6) divided by 1/6
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Tristan has some dimes and some quarters. He has at least 20 coins worth at most $4.25 combined. If Tristan has 10 dimes, determ
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Answer:

The maximum number of quarters that he could have is 13

Step-by-step explanation:

Let x represent the number of quarters he could have. If he has 10 dimes and has at least 20 coins, then

→ x + 10 >= 20

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His coins worth at most $4.25. Also, it is known that 1 dollar is equal to 100 cents, 1 dime is equal to 10 cents and 1 quarter is equal to 25 cents.

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The maximum value of x is 13

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