MATHEMATICS COLLEGE

The filling variance for boxes of cereal is designed to be .02 or less. A sample of 41 boxes of cereal shows a sample standard deviation of .16 ounces. Use α = .05 to determine whether the variance in the cereal box fillings is exceeding the design specification.

Answers

Answer 1

Answer:

Answer:

$\chi^2 =(41-1)/(0.02) 0.0256 =51.2$

$p_v =P(\chi^2_(40) >51.2)=0.1104$

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(51.2,40,TRUE)"

If we compare the p value and the significance level provided 0.05 we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population variance is not significantly higher than 0.02, so there is no a violation of the specifications.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=41$ represent the sample size

$\alpha=0.05$ represent the confidence level

$s^2 =0.16^2 =0.0256$ represent the sample variance obtained

$\sigma^2_0 =0.02$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is higher than the standard of 0.02, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \leq 0.02$

Alternative hypothesis: $\sigma^2 >0.02$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =(n-1)/(\sigma^2_0) s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =(41-1)/(0.02) 0.0256 =51.2$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case $df = 41-1=40$ . And since is a right tailed test the p value would be given by:

$p_v =P(\chi^2_(40) >51.2)=0.1104$

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(51.2,40,TRUE)"

Conclusion

Related Questions

If you flip three fair coins, what is the probability that you’ll get two tails and one head in any order?
Which of these shows line of symmetry?Select the three correct answers.
The distance between -6 and 15 on a number line is 9?
According to CNN business partner Careerbuilder, the average starting salary for accounting graduates in 2018 was at least $57,413. Suppose that the American Society for Certified Public Accountants planned to test this claim by randomly sampling 200 accountants who graduated in 2018. State the appropriate null and alternative hypotheses.
Which number is both a factor and a multiple of 14

How does the number of solutions of a system depend on ranks of the coefficient matrix and the augmented matrix?

Answers

Answer:

The number of solutions of a system is given by the number of different variables in the system, this number has to be the same as the number of independent equations. The coefficients and the augmented matrix of the system show these values in a matrix form. A system has a unique solution when the rank of both matrixes and the number o variables in the system are the same.

Step-by-step explanation:

For example, the following system has 2 different variables, x and y.

$x+y=1\nx+2y=5$

In order to find a unique solution to the system, the number of independent equations and variables in the system must be the same In the previous example, you have 2 independent equations and 2 variables, then the solution of the system is unique.

The rank of a matrix is the dimension of the vector generated by the columns, in other words, the rank is the number of independent columns of the matrix.

According to Rouché-Capelli Theorem, a system of equations is inconsistent if the rank of the augmented matrix is greater than the rank of the coefficient matrix. The inconsistency of the system is because you can't find a combination of the variables that will solve the system.

ΔABC is a right triangle and ∠B is a right angle. If sin ∠A = 3/5, then what is the ratio for tan ∠C?

Answers

Answer:

$Tan \ \angle C=(3)/(4)$

Step-by-step explanation:

-The sine of an angle in a right triangle is given as:

$Sin \ \theta=(Opposite)/(Hypotenuse)\n\n\therefore Sin \ \angle A=(3)/(5)$

-From this Trigonometric ratio, we calculate the length of the adjacent as:

$b^2+h^2=H^2\n\nb^2=5^2-3^2\n\nb^=4\n\n\therefore Adjacent=4$

We then calculate tan ∠C

$Tan \ \ theta=(Opposite)/(Adjacent)\n\nTan \ \angle C=(3)/(4)$

Answer:

4/3

Step-by-step explanation:

The right triangle is a 3-4-5 triangle- the opposite side of a is 3 (based on 3/5 which is opp/hyp) and the hypnotuse is 5. The ohter side is 4 no matter how it is solved individually. For tan, it is opp/adj so the opp of angle c is 4 and the adj is 3. Therefore it is 4/3. :D The other person flipped it.

Listed are 32 ages for Academy Award winning best actors in order from smallest to largest. (Round your answers to the nearest whole number.) 18; 18; 21; 22; 25; 26; 27; 29; 30; 31; 31; 33; 36; 37; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77

(a) Find the percentile of 37. th percentile
(b) Find the percentile of 72. th percentile

Answers

Answer:

a) 37th percentile: 33 years

b) 72nd percentile: 62 years

Step-by-step explanation:

The kth percentile divides the data into two: on the one hand the lowest k% of the data, and on the other the (1-k)% higher of the data.

For the list provided, the 37th percentile falls to the age of 33. This means that 37% of the data are for ages under 33 years.

The 72nd percentile falls at the age of 62 (72% of the ages fall below 62 years).

AGE PERCENTILE

18 6%

21 9%

22 13%

25 16%

26 19%

27 22%

29 25%

30 28%

31 34%

33 38%

36 41%

37 47%

41 50%

42 53%

47 56%

52 59%

55 63%

57 66%

58 69%

62 72%

64 75%

67 78%

69 81%

71 84%

72 88%

73 91%

74 94%

76 97%

77 100%

Final answer:

The percentile rank of 37 among Academy Award-winning best actors is the 45th percentile, and the percentile rank of 72 is the 87th percentile. These are determined by their positions in the ordered list and the total number of ages listed.

Explanation:

Finding the Percentiles of Ages for Academy Award-winning Best Actors

To find the percentile for a given age in a sorted list, use the formula:

Percentile Rank = (Number of values below your score + 0.5) / Total number of scores x 100

a. To find the percentile of 37 from the list of ages, we must first locate 37 within the ordered list. There are two values of 37, so we use the position of the second 37 for our calculation since it is the last occurrence of that value. This position is 15th in the list. Using the percentile rank formula, we calculate:

Percentile Rank of 37 = (14 + 0.5) / 32 x 100 = 45th percentile (rounded to the nearest whole number).

b. To find the percentile of 72, we find the position of 72, which is 28th in the list. Using the same formula:

Percentile Rank of 72 = (27 + 0.5) / 32 x 100 = 87th percentile (rounded to the nearest whole number).

Therefore, an actor who won the Academy Award at age 37 would be in the 45th percentile of ages of all such actors, while an actor who won at age 72 would be in the 87th percentile.

A calzone is divided into 24 equal pieces. Sophie and Glenn each ate one-fourthof the calzone on Saturday. The next day, Glenn ate one-sixth
of the calzone that was leftover. How many of the pieces of the original calzone remain? Explain your reasoning.

Answers

Answer:

10 pieces

Step-by-step explanation:

Total no. of pieces of calzone = 24

No of pieces of calzone eaten by sophie = 1/4 of Total no. of pieces of calzone = 1/4 of 24 = (1/4)*24= 6 pieces.

No of pieces of calzone eaten by Glenn = 1/4 of Total no. of pieces of calzone = 1/4 of 24 = (1/4)*24= 6 pieces.

Total no of pieces eaten by both of them on saturday = 12.

No of pieces of calzone left = 24-12 = 12

_______________________________________________

No of pieces of calzone eaten by Glenn on next day = 1/6 of Total no. of pieces of calzone left= 1/6 of 12 = (1/6)*12= 2 pieces

No of pieces of calzone left now after Glenn ate 2 of them = 12-2 = 10.

Thus 10 pieces of original calzone are left .

Salma sold 600 liters of soda at a baseball game. How much is this in milliliters?Be sure to include the correct unit in your answer.
mL
mg
kL
kg

Answers

Final answer:

600 liters of soda is equal to 600,000 milliliters.

Explanation:

To convert liters to milliliters, we multiply by 1000 since there are 1000 milliliters in one liter. So, 600 liters of soda is equal to 600,000 milliliters.

Learn more about Converting units here:

brainly.com/question/31429209

Which of the following is equivalent to 46? 6 + 6 + 6 + 6 4 • 4 • 4 • 4 • 4 • 4 4 + 4 + 4 + 4 + 4 + 4 6 • 6 • 6 • 6

Answers

Answer:

None

Step-by-step explanation:

(4)^6 (6)^4 6+6+6+6 4+4+4+4+4+4

4096 1296 24 24

Answer: none

Step-by-step explanation:

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A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.Suppose the paper is 7"-wide by 9"-long.a. Estimate the maximum volume for this box?b. What cutout length produces the maximum volume?