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the “Snoopy” cartoon

  1. Reference the “Snoopy” cartoon above.
    1. State the null and alternative hypothesis that Charlie Brown should make re: the above Situation. Hint: Cast this in terms of a “research hypothesis”, and specifically, reference frame 4, 5 and 9.

Null Hypothesis: Involuntary Muscle Spasm at the same moment of kicking the ball could not occur.

Alternate Hypothesis: Involuntary Muscle Spasm at the same moment of kicking the ball could occur.

The hypothesis was derived by the reference frames 4,5 and 9 these frames in the cartoon state the key element that is under research and null hypothesis is obviously a denial of the fact that is under investigation.

  • Differentiate between Type I and Type II errors.

The Type I error is the wrong rejection of a null hypothesis. In this case if the snoopy cartoon depicts that involuntary muscle spasm could occur, when it cannot, is a type I error.

Type II error is reverse of Type I error. If Snoopy accepts that the muscle spasm cannot occur, when it can, is a type II error. In short type II error is a research process where a null hypothesis has to be rejected but, is not.

  • What type of error, of any, did Charlie Brown make? Explain your answer.

Charlie Brown made a type II error, as heaccepted the null hypothesis of the nonoccurrence of the involuntary muscle spasm at moment of the kick so he tried to kick the ball.

  • Explain in common English what you mean when you say 99% confidence interval

Confidence Interval is the trust of data in accordance with the prospects of research being conducted. 99% confidence interval indicates that the data is to be tested if it is 99% aligned with the research and its flow.

  • Since it is possible to test statistical hypothesis with any size sample, explain why a researcher would prefer larger sample size?

A larger sample size denotes that it is easier to apply the research to the overall area of analysis.

  • Usesimple plain English to define and distinguish between the following:
    • P-Value and Alpha-Value:

The data is tested via p value value is for the variables, in short, and Alpha Value is for the questionnaire or the tool used for measuring it.

  • Standard deviation and standard error of the mean:

Standard deviation tells the ability of the sample to change and standard error shows that if the calculation of means is correct.

  • You are confronted with a set of data on the blood cell count change of patients treated with new drug. You wish to statistically evaluate whether the drug has caused a significant change in cell count. What all you must do before actually doing the evaluation? (list proper sequence the specific steps you must take before conducting the statistical test to evaluate the hypothesis). (NOTE: you might want to mention the use of alpha, beta, and P-values).

Step1: A method should be devised for this evaluation. Including development of hypothesis and test mechanism.

Step2: Test study should be conducted in order to verify the tools (Alpha Value)

Step3: A proper study with a representative sample should be conducted.

Step4: Results should be regressed in such a way that New Drug usage is the independent variable and blood cell count is the dependent variable.

Step5: Significance should be tested and alpha and beta should be analyzed. Significance is the basis of acceptance or rejection of null hypothesis. Alpha denotes the blood count independent of drug and beta denotes the relationship between drug usage and blood count. If beta is positive, this indicates that with drug usage blood count increases and if it is negative, this indicates that the drug usage reduces the blood cells in a human body.

  • A nutrition researcher believed that the mean protein intake of students on campus was at least 65 grams/day. One hundred randomly chosen individuals kept 21-day diet record, and their average daily protein intake (in grams) was recorded. The mean intake was 61.9 (+or-) 15.9 grams/day.       
    • Formulate an appropriate null and alternative hypothesis relative to the information presented. Explain you rational for your response

H0: The Mean nutrition intake of the sample is not the same as that of the campus

H1: The Mean nutrition intake of the sample and the population is the same.

The rationale behind this hypothesis is that if the null hypothesis is rejected it can be concluded that the sample represents the population and if it is not there that null hypothesis would be rejected

  • A Mean of five picocuries/liter or below is considered a safe level of radioactivity in drinking water. Ten Samples of drinking water were collected from a reservoir near a nuclear power plant in order to monitor radioactivity levels. The following measurements were recorded (in picocuries/liter):

5.2, 4.7, 6.1, 4.1, 5.5, 4.5, 5.1, 6.0, 5.3, 4.9. The mean of this sample is 5.14± 0.629 picocuries/liter.

  1. Compute a 95% confidence interval for the population mean. Express your results as upper limit and lower limit ± CI. Show all your work.
Data  
5.2  
4.7  
6.1  
4.1  
5.5  
4.5  
5.1  
6  
5.3  
4.9  
Mean 5.14
SD 0.629285
 
Upper Limit 5.769285
Lower Limit 4.510715

Confidence of interval

Mean = 5.14

SD     = 0.63

Standard error = 0.63/ √ 10

                        = 0.63/3.16

                        = 0.1994

Margin of error = S.D* 2

                          = 0.63*2

                          = 1.26

Confidence interval = 5.14+1.26, 5.14-1.26

                                 = 6.4 to 3.88

  • On the basis of these results, can it be concluded that the levels of radioactivity in the drinking supply are unsafe? State clearly your assumption(s) as well as the appropriate null and alternative hypotheses.

The above results show that the sample’s upper and lower limit lie outside the accepted water levels for the region. Therefore, hypotheses are as follows

H0: The Drinking water in the lake is not safe for drinking.

H1: The Drinking water in the lake is safe for drinking.

In this case null hypothesis is accepted due to the above given facts.
Sampling was not random as all the trees were selected from the selected geographic area. This can also be seen that the potential trees are the whole lot of them.

  • Identify whether the following variables are numerical or categorical. If numerical, state whether the variable is discrete or continuous. If categorical, state whether the variable is nominal or ordinal.
  Numerical Scale Categorical State
  Discrete Continuous Nominal Ordinal
Number of Sexual Partners in a year by college students        
Petal Area of Rose Flowers        
Key on the musical scale        
Heart beats per minute of Tour de France Cyclists        
Stage of Fruit ripeness (under ripe, ripe, over ripe)        
Angle of flower orientation relative to position of sun        
Letter grade on high school report card        
Tree Species        
Year of Birth        
  • The Average age of pinon Juniper trees in the coastal region of California was investigated by placing a 10-hectare plot randomly on a distribution map of the tree in California using a computer. Researchers then record the location of the random plot, found it in the field, and flagged it using compass and measuring tape. They then proceeded to measure the age of every pinon juniper tree within the 10-hectare plot. The average age within the plot was used to estimate the average age of the whole California Population
    • What is the population of interest in this study?

The population of interest in this study is the California Population of Pinon Juniper trees.

  • Were the trees sampled randomly from this population? Why or Why not?

No this was not completely random sampling though this did select a 10 hectare plot randomly by the trees in that region do not necessarily depict the whole lot of population, in fact this does not proclaim to be the ultimate random sample.

  1. Can environmental factors influence the incidence of Schizophrenia? A recent project measured incidence of the disease among children born in a region of eastern China. 192 of 13,748 babies born in the midst of a severe famine in the region in 1960 later developed schizophrenia. This compared with 483 schizophrenics out of 59088 births in 1956, before the famine, and 695 out of 83,536 births in 1965, after the famine (St Claire et al. (2005)).
    1. What two variables are compared in this example?

The variables compared in this example are births during famine and development of schizophrenia.

  • Are the variables numerical or categorical? If numerical, are they continuous or discrete; if categorical are they nominal or ordinal?

The variable of births during famine, is discrete variable in the numerical category and the variable of development of schizophrenia is nominal in the categorical variable.