Please help!!!!!!!!!!!!!!!

By law, an industrial plant can discharge not more than 500 gallons of waste water per hour, on the average, into a neighboring

Alisiya [41]

Answer:

We conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

Step-by-step explanation:

We are given that an industrial plant can discharge not more than 500 gallons of wastewater per hour, on average, into a neighboring lake.

Four one-hour periods are selected randomly over a period of one week. The following are observed:

1384, 683, 1534, 405

Let $\mu$ = population average gallons of wastewater discharged per hour

So, Null Hypothesis, $H_0$ : $\mu \leq$ 500 gallons {means that not more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

Alternate Hypothesis, $H_A$ : $\mu$ > 500 gallons {means that more than 500 gallons of wastewater per hour, on the average, is discharged into a neighboring lake}

The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean = $\frac{\sum X}{n}$ = 1001.5 gallons

s = sample standard deviation = $\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }$ = 543.79

n = sample of periods = 4

So, the test statistics = $\frac{1001.5-500}{\frac{543.79}{\sqrt{4} } }$ ~ $t_3$

= 1.844

The value of t-test statistics is 1.844.

Since in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the t table gives a critical value of 2.353 at 3 degrees of freedom for the right-tailed test.

Since the value of our test statistics is less than the critical value of z as 1.844 < 2.353, so we have insufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that not more than 500 gallons of wastewater per hour, on average, is discharged into a neighboring lake.

4 0

3 years ago

An urn contains 17 white balls and 20 red balls. A sample of four balls is selected at random from the urn. What is the probabil

Minchanka [31]

The probability that the sample of four balls contains two white balls and two red balls is 0.39.

Let E be an event a sample of selecting four balls from an urn are two red balls and two white balls.

According to the given question.

Total number of marbles in an urn = 17 + 20 = 37

Total number of white marbles = 17

Total number of red marbles = 20

Now, the number of ways of selecting four marbles form an urn = $^{37} C_{4}$

And, number of ways of selecting 2 white and two red marbles = $^{17} C_{2} \times\ ^{20} C_{2}$

As, we know that probability of an event is calculated by taking the ratio of total number of favorable outcomes to the total number of outcomes.

Therefore, the probability that the sample of four balls contains two white balls and two red balls is given by

$P(E) = \frac{^{20}C_{2} \times ^{17}C_{2} }{^{37}C_{4} }$

$\implies P(E) = \frac{\frac{20!\times 17!}{2!18!(2!!15!)} }{\frac{37!}{4!33!} }$

$\implies P(E) = \frac{\frac{20(19)(17)(16)}{2(2)} }{\frac{37(36)(35)(34)}{(4)(3)(2)} }$

⇒ P(E) = 5(19)(17)(16)/(37(3)(35)(17))

⇒ P(E) = 19(16)/37(3)(7)

⇒ P(E) = 304/777

⇒ P(E) = 0.39

Hence, the probability that the sample of four balls contains two white balls and two red balls is 0.39.

Find out more information about probability here:

brainly.com/question/11234923

#SPJ4

8 0

2 years ago

In Miami, the number of highway accidents increased by 20% over a four year period. How many accidents were there in 2013 if the

scZoUnD [109]

Answer:

Step-by-step explanation:

20/100 * 5,120 = 1024

Number of cases in 2013 = 1024 + 5120 = 6,144 cases

5 0

3 years ago

When you want to sell stock, you either call or visit the stock market.

Andrej [43]

False because you don’t call or visit the stock market .

7 0

4 years ago

Read 2 more answers

If 2 1/4 pounds of bananas cost $1.89 what is the cost per pound

Nikitich [7]

84 cents a pound divide 2 1/4 by 1.89 equals 0.84

6 0

3 years ago

Read 2 more answers