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
ruslelena [56]
2 years ago
12

The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5

for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = 0.32 and that x = 5.24. (Use α = 0.05.) (a) Does this indicate conclusively that the true average percentage differs from 5.5?
State the appropriate null and alternative hypotheses.

H0: μ = 5.5
Ha: μ > 5.5H0: μ = 5.5
Ha: μ ≥ 5.5 H0: μ = 5.5
Ha: μ < 5.5H0: μ = 5.5
Ha: μ ≠ 5.5
Mathematics
1 answer:
miskamm [114]2 years ago
7 0

Answer:  

z=-3.25

p_v =2*P(z  

Step-by-step explanation:  

1) Data given and notation  

\bar X=5.24 represent the mean production for the sample  

\sigma=0.32 represent the sample standard deviation for the sample  

n=16 sample size  

\mu_o =5.5 represent the value that we want to test  

\alph=0.05a represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

p_v represent the p value for the test (variable of interest)  

Part a: State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean production is different from 5.5 tons, the system of hypothesis would be:  

Null hypothesis:\mu =5.5  

Alternative hypothesis:\mu \neq 5.5  

If we analyze the info given we know the population deviation so is better 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{s}{\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".  

Calculate the statistic  

We can replace in formula (1) the info given like this:  

z=\frac{5.24-5.5}{\frac{0.32}{\sqrt{16}}}=-3.25  

P-value

Since this is a two side test the p value would be:  

p_v =2*P(z  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the production its significant different compared to the desired percentage of SiO2 of 5.5 at 5% of signficance.  

You might be interested in
Which statement is correct?
Arisa [49]

Answer:

2.06 \times 10^-^2 = 206

1.88 \times 10^-^1 = 18.8

206 \times 18.8 = 3,872.8

7.69 \times 10^-^2 = 769

2.3 \times 10^-^5  = 230,000

=\frac{769}{230000}

= 0.00334

therefore,

3,872.80 > 0.00334

Step-by-step explanation:

Which statement is correct?

(2.06x102x1.88 x 10-1) <7.69x 10

2.3x10-5

(2.06 x 10-2)(1.88 x 10-1) 7.69x 10-

2.3x10-5

7.69 x 10"

(2.06 x 10-2x1.88x10-)>

2.3x10-5

(2.06x 10-2X(1.88x 10-1)-7.69x104

2.3x10-5

Given that;

2.06 \times 10^-^2 = 206

1.88 \times 10^-^1 = 18.8

206 \times 18.8 = 3,872.8

7.69 \times 10^-^2 = 769

2.3 \times 10^-^5  = 230,000

=\frac{769}{230000}

= 0.00334

therefore,

3,872.80 > 0.00334

7 0
3 years ago
Cathrine has £7000 to invest.
Anvisha [2.4K]
Since this is a compound interest problem, you have to take note that the amount Catherine will get per year is not the same. It will increase per year since it is compounded. So first, we get the amount after one year. This will be 7000 x 0.04 which is 280 plus 7280. In the second year, she will get 7571 (7280 x 0.04 + 7280). In the third year, she will get 7874 (7571 x 0.04 + 7571). In the fourth year, she will get 8189 (7874 x 0.04 + 7874). And finally in the fifth year, she will get 8517 (8189 x 0.04 +8189). So after five years, she has 8517
4 0
3 years ago
Whats the slope of (3,-4), (-18,0)
DochEvi [55]
The answer is -19 because I asked my math teacher and she said-19
8 0
2 years ago
Read 2 more answers
What is the area of this figure?​
lesantik [10]

Answer:

\Huge\boxed {A =859ft^{2} }

Step-by-step explanation:

Hello There!

To solve for the area of this figure we need to split the figure into 3 different parts:

A rectangle with a length of 9 ft and a width of 7 ft

a rectangle with a width of 9ft + 7ft and a length of 25 ft

a rectangle with a width of 18 ft and a length of 22 ft

To find the area of a rectangle we use the formula

A=w*l where w = width and l = length

for the first one we plug in the values

A = 9 * 7

9 * 7 = 63 so the area of the smallest rectangle  is 63ft²

Now lets find the area of the larger rectangle

The dimensions are l = 25 ft and w = 9 + 7 (16 ft)

Now we can plug in the values into the area formula

A = 16 * 25

16*25=400 so the area of the larger rectangle is 400 ft²

Now lets find the area of the last rectangle

The dimensions are l = 22 ft and w = 18 ft

now lets plug in the values to the formula

A = 22 * 18 =396

so the area of the last rectangle is 396 ft²

Finally we want to add all of the areas together

396 + 400 + 63 = 859

So the area of the figure is 859 ft²

7 0
3 years ago
Read 2 more answers
(8 times 10 to the fourth power)+(4 times 10 to the fourth power)
Aliun [14]

Answer:

120,000

Step-by-step explanation:

8 times 10 to the 4th power is 80,000 and 4 times 10 to the 4th power is 40,000 and 80,000 plus 40,000 is 120,000

8 0
3 years ago
Other questions:
  • The ordered pairs model an exponential function, where j is the function name and e is the input variable.
    5·1 answer
  • 5 8 of 48 is equal to 8 15 of some number. What is this number?
    8·1 answer
  • Solve for x -x + 2 = 4
    11·2 answers
  • Determine whether w= 1.8 is a solution to the equation 9.5 = w/0.2
    10·2 answers
  • What is the answer to this equation<br><br> (7x-1)+(9x+5)
    9·1 answer
  • Simplify (3/8 - 6/4) - (9/16 - 3/4)
    15·1 answer
  • Autumn sells laptop computers for $800 each. If she sells 57 computers, how much money does she earn?
    12·1 answer
  • PLZ HELP!!! ILL GIVE YOU BRAINLIEST<br> what is the unit rate for 176 students in 4 buses
    9·1 answer
  • An initial investment of $1000 grows at an interest rate of 4% per year. How long will it take that investment to reach $1,500?
    11·1 answer
  • Elena walked 12 miles. Then she walked 0.25 that distance. How far did she walk altogether? Select all that apply.
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!