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 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.)

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?

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?

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).

a chem 1515 student does the same experiment as the one you will be conducting this week but at a different temperature. She mixes 5.00 mL of 1.00 x 10-3 M solution of Fe(NO3)3 with 5.00 mL of 1.00 x 10-3 M KSCN solution. She finds out the equilibrium concentration of FeSCN2+ at theis condition to be 2.5 x 10-5 M. What is the value of the equilibrium constant for the reaction? Fe3+ (aq) + SCN- (aq) <--> FeSCN2+ (aq)

An experiment was conducted to investigate the effect of extrusion pressure (P) and temperature at extrusion (T) on the strength y of a new type of plastic. Two plastic specimens were prepared for each of five combinations of pressure and temperature. The specimens were then tested in a random order and the breaking strength for each specimen was recorded. The independent variables were coded (transformed) as follows to simplify the calculations: x₁= (P-200)/10, x₂= (T-400)/25. The n=10 data points are listed in the table:

                y                     X₁                  X₂

              5.2                  -2                  2

                5                  -2                  2

              0.3                  -1                 -1

            -0.1                  -1                 -1

            -1.2                   0                  -2

            -1.1                   0                  -2

              2.2                  1                  -1

2                   1                  -1

6.2________2 ________2

              6.1                  2                   2

!                                                               

1. Find the least-squares regression equation of the form y = β₀ + β₁x₁ + β₂x₂ + ε (you may use a calculator or any software that can perform operations with matrices).
2. Does the model contribute information for the prediction of y? Test using α=0.10.
3. Suppose that we are interested in an interval estimate for the strength of plastic for the following combination of pressure and temperature: x₁=1 and x₂=1. Would a confidence interval or a prediction interval be more appropriate in this situation? Calculate this interval using α=0.01.

An experiment was conducted to see the effectiveness of two antidotes to three different doses of a toxin. The antidote was given to a different sample of participants five minutes after the toxin. Thirty minutes later the response was measured as the concentration in the blood. What can the researchers conclude with an α of 0.01?

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Obtain/compute the appropriate values to make a decision about H₀.
Antidote: critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Dose: critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0


c) Compute the corresponding effect size(s) and indicate magnitude(s).
Antidote: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Dose: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


d) Make an interpretation based on the results.

There is an antidote difference in blood concentration.

There is no antidote difference in blood concentration.    

There is a dose difference in blood concentration.

There is no dose different in blood concentration.    

There is an antidote by dose interaction in blood concentration.

There is no antidote by dose interaction in blood concentration.    

An experiment examined the impact of THC (the active ingredient in marijuana) on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Subjects came to the lab 3 times, each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC (a placebo). The order of the conditions was randomized in a double-blind design.At the start of each session, no subject reported being “high.” After smoking the cigarette, participants rated how “high” they felt, using a positive continuous scale (0 representing not at all “high”). For the placebo condition, participants reported a mean “high” feeling of 11.3, with a standard deviation of 15.5. Is there evidence of a significant placebo effect, with subject feeling significantly “high” after smoking a placebo marijuana cigarette?

**********************PLEASE SHOW WORK!!!!*******************************

What is the appropriate statistic to test this hypothesis? What is its value?

What is the P-value for the appropriate test? Specify the distribution used and all relevant parameters.

An experiment was planned to compare the mean time (in days) required to recover from a common cold for persons given a daily dose of 4 milligrams (mg) of vitamin C, μ₂, versus those who were not, μ₁. Suppose that 32 adults were randomly selected for each treatment category and that the mean recovery times and standard deviations for the two groups were as follows.

Conduct the statistical test of the null hypothesis in part (a) and state your conclusion. Test using

α = 0.05.

(Round your answer to two decimal places.)

Find the test statistic.

z =

Find the rejection region. (Round your answers to two decimal places. If the test is one-tailed, enter NONE for the unused region.)

z > z <