Question

In: Math

Suppose you are conducting an experiment and inject a drug into three mice. Their times for...

Suppose you are conducting an experiment and inject a drug into three mice. Their times for running a maze are 8, 10, and 15 seconds; the times for two control mice (i.e. not injected with the drug) are 5 and 9 seconds.

Perform a two-sided permutation rest to determine if there is a statistically significant difference between mean maze completion time with the drug and without the drug.

Solutions

Expert Solution

We will perform two tailed t-test if the underlying distribution assumptions are assumed to be in place.

  • State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

    Null hypothesis: μ1 - μ2 = 0 or μ1 = μ2

    Alternative hypothesis: μ1 - μ2 ≠ 0

    Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
  • There is missing information regarding the significance level but lets assume it is 0.10 i.e. 10%. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
  • Calculate Standord Error (SE): Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

    SE = sqrt[(s1^2/n1) + (s2^2/n2)]

= 2.89

  • Calculate Degrees of freedom (DF):

DF=(s1^2/n1 + s2^2/n2)^2 / { [ (s1^2 / n1)^2 / (n1 - 1) ] + [ (s2^2 / n2)^2 / (n2 - 1) ] }

= 2.74 (rounded to 3)

  • Test statistic. The test statistic is a t statistic (t) defined by the following equation.

    t = [ (x1 - x2) - d ] / SE

where x and x2 are two sample means and d is the difference between two means we want to perform statistical significant test for. In our case because we want to compare two means, this is 0.

hence t = (11-7)/2.89 = 1.39

  • Using the t-distibution we find out the probablity of P(t < -1.39) = .1294 and P(t > 1.39) =.1294

    which is greater than the statistical significance level we assumed (.10). hence fail to reject the null hypothesis. which means that the drug effect cannot be ascertained at the significance level (10%).


Related Solutions

Suppose you have an experiment where you flip a coin three times. You then count the...
Suppose you have an experiment where you flip a coin three times. You then count the number of heads. State the random variable. Write the probability distribution for the number of heads. Draw a histogram for the number of heads. Find the mean number of heads. Find the variance for the number of heads. Find the standard deviation for the number of heads. Find the probability of having two or more number of heads. Is it unusual to flip two...
Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment...
Suppose the owners of a new bed and breakfast establishment are interested in conducting an experiment to determine effective advertisement strategies for increasing the number of reservations. The bed and breakfast owners intend to rotate advertisements for 12 weeks between a travel website, a travel magazine and a local billboard. Customers making reservations will be asked if they saw the advertisement. In this experiment, the independent variable has how many levels? A) 1 B) 2 C) 3 D) 4 E)...
conduct an experiment in which you have to flip a coin three times. after doing that,...
conduct an experiment in which you have to flip a coin three times. after doing that, Compile the results & submit a report consisting of the following topics.... 1. state sample space. 2. find out probability of getting exactly 2 heads. make sure you state that event space. 3. find the probability of getting at least 2 heads. make sure you stay there. 4.Find the probability of giving an odd number of heads. make sure you state the event space....
2- In a research laboratory you are doing an experiment on mice bone to find out...
2- In a research laboratory you are doing an experiment on mice bone to find out enzymatic activity. What would be the best way to prepare your biopsy for this purpose.
Suppose that a scientist was conducting an experiment and decided to transplant GFP-labeled cells from the...
Suppose that a scientist was conducting an experiment and decided to transplant GFP-labeled cells from the dorsal region of a frog embryo at the 120-cell embryonic stage into the putative ventral side of an unlabeled zebrafish embryo of an equivalent developmental stage, state one question the scientist might have been trying to answer. Explain how this experimental design would answer the question you stated. Transplantation could be used to build a fate map of an early embryo. True or False
A random experiment consists of throwing a triangular shape with three faces three times. The first...
A random experiment consists of throwing a triangular shape with three faces three times. The first face has the number 1, the second face has the number 2 and the third face has the letter A. List the sample space of the random experiment.    Assume the faces are equally likely, what is the probability an outcome of experiment has at least one A?                                                                                                   the letter A is three times likely to occur in a throw than the...
An investigator conducts an experiment involving the effects of three levels of a drug on memory....
An investigator conducts an experiment involving the effects of three levels of a drug on memory. 12 subjects are randomly assigned to one of three conditions (0mg, 15mg, 30mg). A different drug level is administered in each condition. Memory is measured 10 minutes after each subject receives the drug. The following scores are recorded. The higher the score, the better the memory. 0mg Drug 6, 10, 8, 11 15mg Drug: 9, 7, 9, 11 30mg Drug: 13, 15, 14, 19...
In one experiment, you have 2 mice of different strains, the first has no mutation or...
In one experiment, you have 2 mice of different strains, the first has no mutation or wild type (WT) and the second is a conditional knockout (KO) of the insulin receptor specifically in skeletal muscle. After an overnight fast, both are fed a glucose solution. One hour later, in both mice blood glucose levels have peaked suggesting that the glucose has been processed through the portal vein and into general circulation. Two hours later, blood glucose levels in the WT...
a chem 1515 student does the same experiment as the one you will be conducting this...
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)
2. Imagine that you are conducting an experiment that compares the effects of drought on photosynthesis...
2. Imagine that you are conducting an experiment that compares the effects of drought on photosynthesis in two species in the family Ericaceae: Vaccinium parvifolium (red huckleberry) and Vaccinium oxycoccos (small cranberry), both native to Oregon. What methods (name 2) could you use to measure water stress or availability in this experiment? Why might you need to know if these plants have either C3 or C4 photosynthesis? Explain. Design a greenhouse experiment that would allow you to address competition between...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT