A physiological experiment was conducted to study the effect of various factors on pulse rate. For one factor, there were 92 subjects, the mean pulse rate of which was 72.87, and the sample standard deviation was 11.01. Consider the following hypotheses: i. H0: m=75 vs. Ha: m> 75, ii. H0: m=75 vs. Ha: m does not =75 where m is the population mean. a). Compute the p-value for each test . b) State the conclusion based on the 5% level of significance.
In: Statistics and Probability
The following data set is taken from an experiment performed at NIST. The purpose is to determine the effect of machining factors on ceramic strength.
Number of observations = 32 (a full 25 factorial design)
Response Variable Y = Mean (over 15 reps) of Ceramic Strength
Factor 1 = Table Speed (2 levels: slow (.025 m/s) and fast (.125 m/s))
Factor 2 = Down Feed Rate (2 levels: slow (.05 mm) and fast (.125 mm))
Factor 3 = Wheel Grit (2 levels: 140/170 and 80/100)
Factor 4 = Direction (2 levels: longitudinal and transverse)
Factor 5 = Batch (2 levels: 1 and 2)
Run the experiment and analyze the results. Determine what 2-way interactions and main effects Plot the main effects and the significant 2-way interactions and add your conclusions.
The design matrix is given in an actual randomized run order:
| (X1:Table Speed) | (X2:Feed Rate) | (X3:Wheel Grit) | (X4:Direction) |
(X5:Batch) |
(Y:Strength) | (Actual Run Order) | |
| -1 | -1 | -1 | -1 | -1 | 476.315 | 17 | |
| 1 | -1 | -1 | -1 | -1 | 505.736 | 30 | |
| -1 | 1 | -1 | -1 | -1 | 491.498 | 14 | |
| 1 | 1 | -1 | -1 | -1 | 466.851 | 8 | |
| -1 | -1 | 1 | -1 | -1 | 492.569 | 32 | |
| 1 | -1 | 1 | -1 | -1 | 449.498 | 20 | |
| -1 | 1 | 1 | -1 | -1 | 485.086 | 26 | |
| 1 | 1 | 1 | -1 | -1 | 468.482 | 24 | |
| -1 | -1 | -1 | 1 | -1 | 344.106 | 10 | |
| 1 | -1 | -1 | 1 | -1 | 332.864 | 16 | |
| -1 | 1 | -1 | 1 | -1 | 335.132 | 27 | |
| 1 | 1 | -1 | 1 | -1 | 397.761 | 18 | |
| -1 | -1 | 1 | 1 | -1 | 311.304 | 3 | |
| 1 | -1 | 1 | 1 | -1 | 287.259 | 19 | |
| -1 | 1 | 1 | 1 | -1 | 299.957 | 31 | |
| 1 | 1 | 1 | 1 | -1 | 344.029 | 15 | |
| -1 | -1 | -1 | -1 | 1 | 425.138 | 12 | |
| 1 | -1 | -1 | -1 | 1 | 434.56 | 1 | |
| -1 | 1 | -1 | -1 | 1 | 427.385 | 4 | |
| 1 | 1 | -1 | -1 | 1 | 446.628 | 23 | |
| -1 | -1 | 1 | -1 | 1 | 409.633 | 2 | |
| 1 | -1 | 1 | -1 | 1 | 410.319 | 28 | |
| -1 | 1 | 1 | -1 | 1 | 421.169 | 11 | |
| 1 | 1 | 1 | -1 | 1 | 425.817 | 9 | |
| -1 | -1 | -1 | 1 | 1 | 310.03 | 25 | |
| 1 | -1 | -1 | 1 | 1 | 304.087 | 21 | |
| -1 | 1 | -1 | 1 | 1 | 292.362 | 6 | |
| 1 | 1 | -1 | 1 | 1 | 357.588 | 7 | |
| -1 | -1 | 1 | 1 | 1 | 274.477 | 5 | |
| 1 | -1 | 1 | 1 | 1 | 240.254 | 13 | |
| -1 | 1 | 1 | 1 | 1 | 269.864 | 22 | |
| 1 | 1 | 1 | 1 | 1 | 312.711 | 29 |
In: Statistics and Probability
A factorial experiment was designed to test for any significant differences in the time needed to perform English to foreign language translations with two computerized language translators. Because the type of language translated was also considered a significant factor, translations were made with both systems for three different languages: Spanish, French, and German. Use the following data for translation time in hours.
| Language | |||
| Spanish | French | German | |
| System 1 | 6 | 12 | 11 |
| 10 | 16 | 15 | |
| System 2 | 9 | 13 | 17 |
| 13 | 15 | 23 | |
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use = .05.
| Source of Variation | Sum of Squares | Degrees of Freedom | Mean Square | F | p-value |
| Factor A | |||||
| Factor B | |||||
| Interaction | |||||
| Error | |||||
| Total |
In: Statistics and Probability
In a lab experiment; the objective is to titrate NaOH solution into known KHP solution to determine NaOH solution concentration. Using the same NaOH solution we titrate an UKNOWN sample of KHP. I am having trouble calculating the % purity of my sample.
mol of NaOH USED TO TITRATE IN ALIQUOT: 0.001289mol (trial 1), 0.001289mol (trial 2), 0.001291mol (trial 3)
mol of KHP in aliquot: I calculated as 1:1 ratio THEREFORE 0.001289mol (trial 1), 0.001289mol (trial 2), 0.001291mol (trial 3) - is this correct?
mol of KHP per mL: I calculated as 6.445*10^-5 (trial 1), 6.445*10^-5 (trial 2), 6.455*10^-5 (trial 3)
average moles of KHP per mL: trial 1 + trial 2 + trial 3 = answer / 3 = 6.448*10^-5 average moles KHP per mL.
total moles of KHP in volumetric flask: volumetric flask is 100mL: I calculated as 0.006448mol
PLEASE CHECK MY CALCULATIONS TO MAKE SURE I AM ON THE RIGHT TRACK.
NEXT IS ASKING FOR "MASS OF PURE KHP," does this mean g/mol? or does this mean the mass of pure KHP if it were 0.006448mol of it in the volumetric flask?
LAST IS ASKING FOR % PURITY OF MY SAMPLE. I AM UNABLE TO FIGURE OUT HOW EXACTLY TO CALCULATE THIS WITH MY GIVEN DATA.
Please show how to derive answer. If you need further information please comment, I will reply ASAP. I WILL RATE YOU FOR YOUR ASSISTANCE. THANK YOU!
In: Chemistry
4.27- An experiment was conducted to investigate the filling capability of packaging equipment at a winery in Newberg, Oregon. Twenty bottles of Pinot Gris were randomly selected and the fill volume (in ml) measured. Assume that fill volume has a normal distribution. The data are as follows: 753, 751, 752, 753, 753, 753, 752, 753, 754, 754, 752, 751, 752, 750, 753, 755, 753, 756, 751, and 750.
(a) Do the data support the claim that the standard deviation of
fill volume is less than 1 ml? Use alpha = 0.05
(b) Find a 95% two-sided confidence interval on the standard
deviation of fill volume.
(c) Does it seem reasonable to assume that fill volume has a normal distribution?
In: Statistics and Probability
An experiment is to be carried out to determine the optimal
combination of microwave oven
settings for microwave popcorn. Cooking time has three possible
settings (3,4, and 5 minutes)
and cooking power has two settings (low power, high power). The
response (to be minimized)
is the number of burned plus the number of unpopped kernels.
a. Identify the experimental unit.
b. Identify the experimental factor(s), levels, and any
factor-level combinations if present
In: Statistics and Probability
In an experiment to investigate the performance of four
different brands of spark plugs intended for use on a 125-cc
motorcycle, five plugs of each brand were tested, and the number of
miles (at a constant speed) until failure was observed. A partially
completed ANOVA table is given.
Fill in the missing entries, and test the relevant hypotheses using
a .05 level of significance. (Give the answer to two decimal
places.)
| Source of Variation |
df | Sum of Squares |
Mean Square |
F |
| Treatments | 1 | 2 | 3 | 4 |
| Error | 5 | 236682.04 | 6 | |
| Total | 7 | 313520.78 | ||
In: Statistics and Probability
The table below lists the observed frequencies for all four categories for an experiment.
__________________________
Category 1 2 3 4
___________________________
Observed Frequency 12 14 18 16
_____________________________
The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the expected frequency for the second category?
The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. The expected frequencies for the four categories are:
Category 1:
Category 2:
Category 3:
Category 4:
The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What are the degrees of freedom for this test?
The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. The significance level is 1%. What is the critical value of chi-square? 12.838 13.277 14.860 11.345
The null hypothesis for the goodness-of-fit test is that the proportion of all elements of the population that belong to each of the four categories is the same. What is the value of the test statistic, rounded to three decimal places?
In: Statistics and Probability
Pete is doing a science-experiment and have decided to work on it until it succeeds. The chance of success on any given day is 0.001. Let X be the number of days until he succeeds. Which probability distribution does X have? What is E(X)? What is the probabilty of Pete succeeding in his first year? If he doesn't succeed the first year, what's the probability of success in the second year?
In: Statistics and Probability
An experiment is to flip a coin until a head appears for the first time. Assume the coin may be biased, i.e., assume that the probability the coin turns up heads on a flip is a constant p (0 < p < 1). Let X be the random variable that counts the number of flips needed to see the first head.
(a) Let k ≥ 1 be an integer. Compute the probability mass function (pmf) p(k) = P(X = k).
(b) If p = 1/3 compute P(2 ≤ X < 4) and P(1 < X < 3).
(c) If p = 1/3 compute P(X > 2).
(d) If p = 1/2 compute P(X is even).
In: Statistics and Probability