The Mars candy company claims that the percentage of blue M&Ms [2] candies is 24%. A sample of 200 M&Ms candies was selected and 54 candies were blue.

a) State the null hypothesis and the alternative hypothesis.

b) Test the claim using a significance level of 0.05.

c) State your conclusion. Should the Mars company take corrective action?

When circuit boards used in the manufacture of CD players are tested, the long-run percentage of defectives is 3%. A random sample of size n=23 of boards have been selected and checked.

The chance that the number of defective boards will exceed the mean by 2 standard deviation is: ?

What percentage of resulted Hydrogen in the reaction: CH4 (g) + NH3 (g) --> HCN (g) + 3H2 (g) must be burnt, with formation if H2O (g), to ensure the quantity of heat absorbed in the reaction?

(the answer is: approximately 35%)

Heat of formation : Hf (kJ/mol)

CH4 (g) = -74,7
NH3 (g) = -46,2
HCN (g) = 130,5
H2O (g) = -241,6

Calculate to one decimal place the percentage composition of:

a) KMnO₄

b) If you have 25,490 grams of aluminum oxide, how much aluminum do you have in the compound?

Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. PLEASE HELP WITH QUESTIONS (F) - (I)

In this setting we have Σx = 70, Σy = 589, Σx² = 1280, Σy² = 71,467, and Σxy = 9210.

(a) Find x, y, b, and the equation of the least-squares line. (Round your answers for x and y to two decimal places. Round your least-squares estimates to four decimal places.)

(b) Draw a scatter diagram displaying the data. Graph the least-squares line on your scatter diagram. Be sure to plot the point (x, y).

(c) Find the sample correlation coefficient r and the coefficient of determination. (Round your answers to three decimal places.)

What percentage of variation in y is explained by the least-squares model? (Round your answer to one decimal place.)
86.5 %

(d) Test the claim that the population correlation coefficient ρ is not zero at the 1% level of significance. (Round your test statistic to three decimal places.)

t = 5.057

Find or estimate the P-value of the test statistic.

0.005 < P-value < 0.010
Conclusion

Reject the null hypothesis, there is sufficient evidence that ρ differs from 0.

(e) For a neighborhood with x = 11% change in population in the past few years, predict the change in the crime rate (per 1000 residents). (Round your answer to one decimal place.)
96.8959 crimes per 1000 residents

(f) Find S_e. (Round your answer to three decimal places.)
S_e =

(g) Find an 80% confidence interval for the change in crime rate when the percentage change in population is x = 11%. (Round your answers to one decimal place.)

(h) Test the claim that the slope β of the population least-squares line is not zero at the 1% level of significance. (Round your test statistic to three decimal places.)

t =

Find or estimate the P-value of the test statistic.

P-value > 0.250

0.125 < P-value < 0.250

0.100 < P-value < 0.125

0.075 < P-value < 0.100

0.050 < P-value < 0.075

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

0.0005 < P-value < 0.005

P-value < 0.0005

Conclusion

Reject the null hypothesis, there is sufficient evidence that β differs from 0.

Reject the null hypothesis, there is insufficient evidence that β differs from 0.  

  Fail to reject the null hypothesis, there is sufficient evidence that β differs from 0.

Fail to reject the null hypothesis, there is insufficient evidence that β differs from 0.

(i) Find an 80% confidence interval for β and interpret its meaning. (Round your answers to three decimal places.)

Interpretation

For every percentage point increase in population, the crime rate per 1,000 increases by an amount that falls outside the confidence interval.

For every percentage point increase in population, the crime rate per 1,000 increases by an amount that falls within the confidence interval.  

  For every percentage point decrease in population, the crime rate per 1,000 increases by an amount that falls within the confidence interval.

For every percentage point decrease in population, the crime rate per 1,000 increases by an amount that falls outside the confidence interval.

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78.

(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.)

  ,

(b) Compute a 98% CI for true average porosity of another seam based on 14 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)

  ,

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.31? (Round your answer up to the nearest whole number.)
specimens

(d) What sample size is necessary to estimate true average porosity to within 0.22 with 99% confidence? (Round your answer up to the nearest whole number.)
specimens

The rate at which a machine operator's efficiency, E(t) (expressed as a percentage), changes with respect to time t is given by

dE/dt=35−16t

where t is the number of hours the operator has been at work.

(A) Find E(t), given that the operator's efficiency after working 2 hours is 80% that is, E(2)=80.

Operator's efficiency function E(t)=

(B) What is the operator's efficiency after 77 hours?

Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.78.

(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 19 specimens from the seam was 4.85. (Round your answers to two decimal places.)

  ,

(b) Compute a 98% CI for true average porosity of another seam based on 13 specimens with a sample average porosity of 4.56. (Round your answers to two decimal places.)

  ,

(c) How large a sample size is necessary if the width of the 95% interval is to be 0.3? (Round your answer up to the nearest whole number.)
specimens

(d) What sample size is necessary to estimate true average porosity to within 0.25 with 99% confidence? (Round your answer up to the nearest whole number.)
specimens