1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SOVA2 [1]
3 years ago
6

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a m

ean of 3.59 mg of mercury. (a) State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean. a. H0: μ ≥ 3.5 mg vs. H1: μ < 3.5 mg b. H0: μ ≤ 3.5 mg vs. H1: μ > 3.5 mg c. H0: μ = 3.5 mg vs. H1: μ ≠ 3.5 mg a b c (b) Assuming a known standard deviation of 0.18 mg, calculate the z test statistic to test the manufacturer’s claim. (Round your answer to 2 decimal places.) Test statistic (c) At the 1 percent level of significance (α = .01) does the sample exceed the manufacturer’s claim? Yes No (d) Find the p-value. (Round your answer to 4 decimal places.) p-value
Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

Answer:

(a) Null Hypothesis, H_0 : \mu \leq 3.50 mg  

     Alternate Hypothesis, H_A : \mu > 3.50 mg

(b) The value of z test statistics is 2.50.

(c) We conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

(d) The p-value is 0.0062.

Step-by-step explanation:

We are given that Green Beam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. Assuming a known standard deviation of 0.18 mg.

<u><em /></u>

<u><em>Let </em></u>\mu<u><em> = average mg of mercury in compact fluorescent bulbs.</em></u>

So, Null Hypothesis, H_0 : \mu \leq 3.50 mg     {means that the average mg of mercury in compact fluorescent bulbs is no more than 3.50 mg}

Alternate Hypothesis, H_A : \mu > 3.50 mg     {means that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg}

The test statistics that would be used here <u>One-sample z test</u> <u>statistics</u> 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 mg of mercury = 3.59

            \sigma = population standard deviation = 0.18 mg

            n = sample of bulbs = 25

So, <em><u>test statistics</u></em>  =  \frac{3.59-3.50}{\frac{0.18}{\sqrt{25} } }

                               =  2.50

The value of z test statistics is 2.50.

<u>Now, P-value of the test statistics is given by;</u>

         P-value = P(Z > 2.50) = 1 - P(Z \leq 2.50)

                                             = 1 - 0.9938 = 0.0062

<em />

<em>Now, at 0.01 significance level the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>

Therefore, we conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.

You might be interested in
What is the unit price for the cans of lemonade at each of the stores. The store prices are 3 for 9$
11Alexandr11 [23.1K]
9$ for three cans then 9/3= 3 $ per can
3 0
3 years ago
If the 6 in 14,563 was changed to a 9 ,how much would the value change
AnnyKZ [126]

Answer:

It would change by 30 points

Step-by-step explanation: If you block the rest of the numbers you would see 63 change to 93. 93-63=30 so it would change by 30 points

8 0
3 years ago
Please help me!
ruslelena [56]
I agree with you because theta could be acute or obtuse, and if obtuse, negative value.
3 0
3 years ago
Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz. An ornithologi
il63 [147K]

Answer:

The formula to generate 70% confidence interval is: [\overline{x} - 0.013, \overline{x} + 0.013], in which \overline{x}  is the sample mean.

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.7}{2} = 0.15

Now, we have to find z in the Z-table as such z has a p-value of 1 - \alpha.

That is z with a pvalue of 1 - 0.15 = 0.85, so Z = 1.037.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Assume that body masses of Goldfinch birds follow a normal distribution with standard deviation equal to 0.04 oz.

This means that \sigma = 0.04.

Sample of 10 birds:

This means that n = 10.

The margin of error is of:

M = z\frac{\sigma}{\sqrt{n}}

M = 1.037\frac{0.04}{\sqrt{10}}

M = 0.013

The lower end of the interval is the sample mean of \overline{x} subtracted by M.

The upper end of the interval is the sample mean of \overline{x} added to M.

Then, the formula to generate 70% confidence interval is: [\overline{x} - 0.013, \overline{x} + 0.013], in which \overline{x}  is the sample mean.

8 0
3 years ago
Three playing cards are placed in a row, from left to right. Each card is of a
qaws [65]

Answer:

hifgreeg33ctvtvunu

Step-by-step explanation:

highhb tug 5h6g6g5g5g

8 0
3 years ago
Other questions:
  • Anne has $40,000 in a savings account that earns 3%
    13·1 answer
  • From a point on a river, two boats are driven in opposite directions, one at 6 miles per hour and the other at 10 miles per hour
    5·1 answer
  • Divide square root 9^2 by square root 18y^2
    8·1 answer
  • Which of the following illustrates the truth value of the given conditional statement? The number is an integer, and a rational
    12·2 answers
  • What’s the answer to this?
    11·1 answer
  • The surface area of a right cone is 400.2 m2. The radius of the cone is 6.0 m. Determine the height of the cone to the nearest m
    15·1 answer
  • Write each decimal as a fraction <br> .07<br> .051<br> .473<br> .27<br> .5.37<br> .16.49
    13·1 answer
  • Plllzzzzzzzzzzzzzz helpppppp
    9·1 answer
  • Find the y-intercept and slope of the functions graph, and find the equation for the function
    14·1 answer
  • Location Score Factor (100 points each) Weight A B C Convenience 0.15 89 78 84 Parking facilities 0.20 75 93 98 Display area 0.1
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!