Use R to calculate the following probability from Z distribution. Please Plot 4) as shown.
1) P (z > 1.46) =
2) P (z < -1.56) =
3) P (0.67 ≤ z ≤ 2.41) =
4) [P (x ≥ 13.24) with µ = 11 and σ = 2] =
5) What is the Z value for P(Z > z) = 0.45?
A biology scientist claims that the distribution of the lifespans of their testing animal subjects has a mean of 54 months and a standard deviation of 6 months. Suppose an audit group decides to check the claim by choosing a sample of 50 of these subjects.
1) Assuming that the scientist's claim is true, describe the sampling distribution of the mean lifetime of a sample of 50 subjects.
2) Assuming that the scientist's claim is true, what the probability the audit group's sample has a mean life of 52 or fewer months?
3) Plot your answer using R as shown.
3. Create 15 random numbers that are normally distributed with mean 10 and s.d. 5. Find a 1-sample t-test CI at the 95% level by modifying the ci95 function in seciton01 of lecture5. Did it get it right? Can you generalize the function so that it works for any given level?
4. Based on part 1, find 80%, 95% and 99% confidence interval for the mean for the exec.pay dataset from "UsingR".
5. For the data set rat from "UsingR", do a t-test for mean against 112 using p value. What is your conclusion.
6. Load library "UsingR"
1) Load the Simple dataset "homework". This measures study habits of students from private and public high schools. Make a side-by-side boxplot. Use the appropriate test to test for equality of means at 5% level.
2) What if I want to test do private schools have higher mean score than that of public ones at 5% level
3) Load the Simple data set "corn". Twelve plots of land are divided into two and then one half of each is planted with a new corn seed, the other with the standard. Use the appropriate test to test for equality of means at 1% level.
7. Consider dataset "juul" from library "ISwR".
Are the means of igf1 equal among tanner groups at 5% level?
Please use the six step process to test statistical hypotheses for this research problem.
Note: You need to convert tanner from numeric to factor type and ignore all the NAs.
8. The following ANOVA table was obtained from a balanced completely randomized design:
1. Fill in the blanks in this table
Source
df
SS
MS
Treatments
4
368
Error
25
575
Total (corrected)
29
2. Determine the number of treatments
3. Determine the number of replications per treatment.
4. What is the F statistics value?
5. Perform a hypothesis test to see if there is a difference in the true mean responses among the treatments at α = 0.01. The p-value from the test is 0.012.
9. In a study, among 747 patients exposed to a treatment A, 130 patients were diagnosed with disease D. Out of 661 people exposed to no treatment, 202 were positive with D. Please construct the 2 X 2 table and calculate RR and OR. What conclusion can we draw based on RR?
10. Are exposure and disease status independent in part 1? Please use the 6-step chi-square test to do the analysis at 99% significance level.
11. From ISwR package, retrieve the dateset named "caesar.shoe". Please use help to find out the explanation of the dataset. Then please carry out the 6-step chi-square test to test for independence at 95% significance level.