to evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 42 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 42 plants received 72 grams of this new type of plant food each week for 4 weeks. The number of tomatoes produced by each plant was recorded yielding the following results: X bar=31.35 s=3.865 (a) Assuming that the seedlings chosen are taken from a population which is normally distributed, determine a 95% confidence interval estimate for the average number of tomatoes that would have been produced by all the seedlings in the greenhouse if they have recieved 72 grams of thee new plant food, once a week for 4 weeks. Use three decimals. Lower Bound : Upper Bound : (b) The greenhouse is currently using a plant food called "Supr-Grow". The average number of tomatoes produced by seedlings in the greenhouse with "Supr-Grow" is 32. Based on the interval in (a), should the greenhouse switch to the new plant food? (YES or NO) (c) A researcher has started with a new sample and a given degree of confidence that the average number of tomatoes the seedlings produced on the new plant food is between "33.00628 and 35.89372". Suppose the sample size and standard deviation are the same as given above. What alpha did the researcher use in the construction of this statement? (Input your answer as a decimal)
In: Statistics and Probability
to evaluate the effectiveness of a new type of plant food developed for tomatoes, an experiment was conducted in which a random sample of 42 seedlings was obtained from a large greenhouse having thousands of seedlings. Each of the 42 plants received 72 grams of this new type of plant food each week for 4 weeks. The number of tomatoes produced by each plant was recorded yielding the following results: X bar=31.35 s=3.865 (a) Assuming that the seedlings chosen are taken from a population which is normally distributed, determine a 95% confidence interval estimate for the average number of tomatoes that would have been produced by all the seedlings in the greenhouse if they have recieved 72 grams of thee new plant food, once a week for 4 weeks. Use three decimals. Lower Bound : Upper Bound : (b) The greenhouse is currently using a plant food called "Supr-Grow". The average number of tomatoes produced by seedlings in the greenhouse with "Supr-Grow" is 32. Based on the interval in (a), should the greenhouse switch to the new plant food? (YES or NO) (c) A researcher has started with a new sample and a given degree of confidence that the average number of tomatoes the seedlings produced on the new plant food is between "33.00628 and 35.89372". Suppose the sample size and standard deviation are the same as given above. What alpha did the researcher use in the construction of this statement? (Input your answer as a decimal)
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 | 10 | 9 | 15 |
| 14 | 13 | 19 | |
| System 2 | 7 | 12 | 14 |
| 11 | 14 | 20 | |
Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use alpha= .05 .
Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.
| 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
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 | 8 | 14 | 15 |
| 12 | 18 | 19 | |
| System 2 | 9 | 15 | 15 |
| 13 | 17 | 21 | |
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 | NA | NA | |||
| Total | NA |
In: Statistics and Probability
|
Language |
|||
|
Spanish |
French |
German |
|
|
System 1 |
8 |
10 |
12 |
|
12 |
14 |
16 |
|
|
System 2 |
6 |
14 |
16 |
|
10 |
16 |
22 |
|
Test for any significant differences due to language translator, type of language, and interaction (use a 5% significance level). Please write out all of your equations by hand.
In: Statistics and Probability
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