In an experiment involving the breaking strength of a certain type of thread used in personal flotation devices, one batch of thread was subjected to a heat treatment for 60 seconds and another batch was treated for 120 seconds. The breaking strengths (in N) of ten threads in each batch were measured. The results were 60 seconds: 43 52 52 58 49 52 41 52 56 58 120 seconds: 59 55 59 66 62 55 57 66 66 51 Let μX represent the population mean for threads treated for 120 seconds and let μY represent the population mean for threads treated for 60 seconds. Find a 99% confidence interval for the difference μX−μY . Round down the degrees of freedom to the nearest integer and round the answers to three decimal places.

The 99% confidence interval is

In order to determine the possible effect of chemical treatment on women’s hair, an experiment was conducted. The results are given in the accompanying table

1. a) State the null hypothesis and the alternative hypothesis

2. b) Calculate (and show) the expected frequency for each cell. Place each expected value in parentheses ( ) in the same cell (and to the right) as the observed value to which it corresponds

3. c) Using the formula: X^2= ∑(O-E)^2/(E)  calculate the chi-square value.

4. d) At the 5% level of significance, what is the chi-square critical value?

5. e) What decision would you make?

6. f) Draw a conclusion (in the context of the problem)?

In calculating the percent yield for this experiment, which of following the statements is/are correct?

An experiment studied the efficacy of using 95% ethanol or 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue being cultured. Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25°C for four weeks. The observation reported was the number of uncontaminated eggplant cuttings after the four-week storage.

(a) Are you willing to assume that the underlying variances are equal?

Yes

No    

(b) Using the information from part (a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested? (Use μ₁ for 95% ethanol disinfectant and μ₂ for 20% bleach disinfectant. Use α = 0.05.)

State the null and alternative hypotheses.

H₀: (μ₁ − μ₂) < 0 versus H_a: (μ₁ − μ₂) > 0

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) ≠ 0    

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) > 0

H₀: (μ₁ − μ₂) = 0 versus H_a: (μ₁ − μ₂) < 0

H₀: (μ₁ − μ₂) ≠ 0 versus H_a: (μ₁ − μ₂) = 0

State the test statistic. (Round your answer to three decimal places.)
t =  

State the p-value.

p-value < 0.010

0.010 < p-value < 0.020    

0.020 < p-value < 0.050

0.050 < p-value < 0.100

0.100 < p-value < 0.200

p-value > 0.200

State the conclusion.

H₀ is rejected. There is insufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.

H₀ is not rejected. There is sufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.    

H₀ is not rejected. There is insufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.

H₀ is rejected. There is sufficient evidence to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants used.

This isn't a homework assignment more of a search for advice. The lab experiment that my group is conducting is to separate two mixtures, a solid-solid and a liquid-liquid mixture. Each mixture has 2 separate components. The solid-solid mixture was easy enough, a quick solvent extraction completely separated the two and soon we will do IR, NMR and melting point determination to try to identify the solids.

The liquids however are another problem all in themselves. The mixture is tinted yellow and is translucent. The two liquids are entirely miscible and there seems to be no obvious phycial way to separate them. There is nothing known about the liquids currently except what we've measured;

The mixture is neutral pH

The mixture has at least one aromatic comound

We've been unable to observe a major polarity difference in the mixture, we had time to run 2 TLC plates, one with polar eluent and one with a mixed 75/25 polar/non-polar eluent. The Rf values have overlapped on both so we believe the compounds have similar polarities, we plan on running a few more with different eluents. This is also why we've been unable to determine whether both compounds are aromatic or only one is.

There is a good chance that the compounds are constitutional isomers of each other based on the hints that our TA has been dropping. We're extremely reluctant to attempt a distillation because as far as we can tell the polarities are extremely similar, as it is directly related to boiling point it is unlikely that the boiling points will be different enough to separate the compounds without a professional distillation set-up. We only have microscale organic kits to work with and previous distillations using the kit resulted in major loss of compound if there is any separation at all.

The rules state we cannot use more than 5mL of the unknown mixture total, for all of the tests we utilize. As a result we cannot afford to lose any to faulty processes like distillation.

The Characterizational techniques we are experienced in using are IR, Melting point, boiling point, refractive index, polarimetry. We are NOT allowed to use Mass Spec. and we can ONLY use NMR after we can prove that we are reasonably confident in the identity of our unknowns.

We're out of ideas so we're hoping for some solid advice and discussion. Thank you!

Tools we have access to are;

TLC

Staining Agents

UV lights

Sep. Funnel

Microscale Distillation (not recommended)

Essentially unlimited glassware

Hot plates and ice-baths

Reagents: HCl, NaOH, Sodium Anhydride, various solvents: toluene, hexanes, ethyl acetate, diethyl ether, water, ethanol, methanol.

I highlighted any relevant information regarding the liquids.

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.

Test for any significant differences due to language translator system (Factor A), type of language (Factor B), and interaction. Use .

Complete the following ANOVA table (to 2 decimals, if necessary). Round your p-value to 4 decimal places.

The p-value for Factor A is - Select your answer -less than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 21

What is your conclusion with respect to Factor A?

- Select your answer -Factor A is not significantFactor A is significantItem 22

The p-value for Factor B is - Select your answer -less than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 23

What is your conclusion with respect to Factor B?

- Select your answer -Factor B is not significantFactor B is significantItem 24

The p-value for the interaction of factors A and B is - Select your answer -less than .005between .005 and .0125between .0125 and .025between .025 and .05greater than .05Item 25

What is your conclusion with respect to the interaction of Factors A and B?

- Select your answer -The interaction of factors A and B is not significantThe interaction of factors A and B is significant

In an experiment to determine the effects of conventional and reduced tillage agriculture on crop yield for oats, 3 varieties of oats and two levels of fertilization (0.5 and 1 kg/ acre) were examined using conventional and reduce tillage techniques. Twenty 20 x 60m plots were each partitioned into 6 -10 x 20m subplots and subplots assigned at random to receive a combination of oat variety and fertilizer treatment. Ten of these plots were subjected to conventional tillage practices and 10 were subjected to reduced tillage practices. Each subplot was harvested at seasons' end and crop yield is expressed in bushels/acre. Examine the data provided in the data file oats.csv. Report hypothesis tests for all possible effects.

Data provided in the data file oats.csv. :

Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Thirteen randomly selected plots of land were treated with fertilizer A, and

10

randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results.

Part 1 of 3

Your Answer is correct

Explain why it is necessary to check whether the populations are approximately normal before constructing a confidence interval.

Since the sample size is ▼small, it is necessary to check that the populations are approximately normal.

Part 2 of 3

Your Answer is correct

Following are boxplots of these data. Is it reasonable to assume that the populations are approximately normal?

400 420 440 460 480 500 520 540

360 370 380 390 400 410 420 430 440 450

It ▼is reasonable to assume that the populations are approximately normal.

Part 3 of 3
Construct a  95% confidence interval for the difference between the mean yields for the two types of fertilizer. Let

μ1 denote the mean yield for fertilizer A. Use the TI-84 Plus calculator. Round the answers to one decimal place.

Fertilizer: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Thirteen randomly selected plots of land were treated with fertilizer A, and

10

randomly selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured from each plot. Following are the results.

Part 1 of 3

Your Answer is correct

Explain why it is necessary to check whether the populations are approximately normal before constructing a confidence interval.

Since the sample size is ▼small, it is necessary to check that the populations are approximately normal.

Part 2 of 3

Your Answer is correct

Following are boxplots of these data. Is it reasonable to assume that the populations are approximately normal?

400 420 440 460 480 500 520 540

360 370 380 390 400 410 420 430 440 450

It ▼is reasonable to assume that the populations are approximately normal.

Part 3 of 3
Construct a  95% confidence interval for the difference between the mean yields for the two types of fertilizer. Let

μ1 denote the mean yield for fertilizer A. Use the TI-84 Plus calculator. Round the answers to one decimal place.

An experiment consists of randomly rearranging the 10 letters of the word QUARANTINE
into a sequence of 10 letters, where all possible orders of these 10 letters are equally likely. Find the probability of each of the following events:

(1) the first three letters include no A’s;

(2)  the first three letters or the last three letters (or both) include no A’s;

(3) the fourth letter is the first A;

(4) the first letter and the last letter are the same;

(5) the word ‘QUARANTINE’ is obtained;

(6) the sequence contains the word ‘RAN’.