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earnstyle [38]
3 years ago
8

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.24 mg of mercury. A sample of 25 bulbs shows a m

ean of 3.29 mg of mercury.
(a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean.
Mathematics
1 answer:
amm18123 years ago
3 0

Answer:

Null hypothesis:\mu \leq 3.24  

Alternative hypothesis:\mu > 3.24  

Step-by-step explanation:

1) Previous concepts  and data given

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

A right tailed test (sometimes called an upper test) is when the alternative hypothesis statement contains a greater than (>) symbol.

\bar X=3.29 represent the sample mean  

s represent the sample standard deviation

n represent the sample selected

\alpha significance level  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean for fluorescent bulbs is no more than 3.24 mg of mercury, the system of hypothesis would be:  

Null hypothesis:\mu \leq 3.24  

Alternative hypothesis:\mu > 3.24  

IIf we know the population deviation we can apply a z test to compare the actual mean to the reference value, and the statistic is given by:  

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}  (1)  

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

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what's it look like if like this |__ right /_ acute \__ obtuse

4 0
3 years ago
An oblique cylinder has a diameter of 14 units. The volume of the cylinder is 1,176π cubic units.
Kaylis [27]

Answer:

24 units


Step-by-step explanation:

The volume of the cylinder = πr²x

Where r is the radius of the base and x is the height of the cylinder.

πr²x = 1,176π

π×(14/2)²x = 1,176π

dividing by π both sides,

(14/2)²x = 1,176

7²x = 1,176

49x = 1,176

x = 1,176/49

  = 24 units


7 0
3 years ago
0.24a + 0.5 = 4.5 What does the variable equal
GREYUIT [131]

Answer:

16.66

Step-by-step explanation:

1) eliminate constant first by performing the opposite operation:

0.24a+0.5-0.5=4.5-0.5

0.24a=4.0

divide both sides by 0.24

a=16.66

4 0
3 years ago
Read 2 more answers
Solve for X .... -3(x-5)>18
Ilya [14]

Answer:

x<-1

Step-by-step explanation:

We multiply by -1 of both sides and change the sense of inequality:

(-1)*(-3(x-5))>(-1)*18

3(x-5)<-18

3 passes by dividing

x-5<-18/3

x-5<-6

5 goes by adding:

x<-6+5

x<-1

6 0
3 years ago
The amount of time a certain brand of light bulb lasts is normally distribued with a mean of 1300 hours and a standard deviation
Bezzdna [24]

Answer:

The interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

Step-by-step explanation:

In statistics, the 68–95–99.7 rule, also recognized as the Empirical rule, is a shortcut used to recall that 68%, 95% and 99.7% of the values lie within one, two and three standard deviations of the mean, respectively.

Then,

  • P (µ - σ < X < µ + σ) = 0.68
  • P (µ - 2σ < X < µ + 2σ) = 0.95
  • P (µ - 3σ < X < µ + 3σ) = 0.997

he random variable <em>X</em> can be defined as the  amount of time a certain brand of light bulb lasts.

The random variable <em>X</em> is normally distributed with parameters <em>µ</em> = 1300 hours and <em>σ</em> = 90 hours.

Compute the interval of hours that represents the lifespan of the middle 68% of light bulbs as follows:

P (\mu - \sigma < X < \mu + \sigma) = 0.68\\\\P(1300-90

Thus, the interval of hours that represents the lifespan of the middle 68% of light bulbs is 1210 hours - 1390 hours.

4 0
3 years ago
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