A study is conducted to see the effectiveness of two COVID 19 vaccines: A and B. Vaccine A works effectively on 205 people in a sample of 220. Vaccine B works effectively on 585 people out of a sample of 650. Construct a 95% confidence interval for the difference in proportion of people treated between those who take vaccine A and those who take vaccine B. Hint: Please keep to at least 4 places past the decimal in calculations! (- 0.0087, 0.0723)

Suppose a researcher is interested in a new treatment plan for CD4 cell count in immune-compromised patients with HIV. In order to investigate the new drug, the researcher gathers a group of 25 individuals with a mean CD4 count of 335 cells/mm3 after treatment with a standard deviation of 12.1. Test the hypothesis that the mean CD4 count goal is not 329.28 cells/mm3. Perform a two-way directional test, complete the 5 step process and calculate the appropriate confidence interval. (Use an alpha level of 0.01)

Prior to an intensive TV advertising campaign, the producers of Nike athletic shoes find that 29 of a random sample of 200 upper-income adults are aware of their new leisure shoe line.  A second random sample of 300 such adults is taken after the campaign.  Now 96 of the persons sampled can identify the new line.  Is the increase in the proportion of upper income adults showing brand awareness significant?  Test the claim using alpha = .05.

Suppose a marketing company randomly surveyed 404 households and found that in 214 of them, the woman made the majority of the purchasing decisions. Construct a 90% confidence interval for the population proportion of households where the women make the majority of the purchasing decisions.p'=α2=zα2=Margin of Error: E=We are 90% confident that the proportion of households in the population where women make the majority of purchasing decisions is between___ and ___.

A manufacturer of a new medication on the market for Parkinson's disease makes a claim that the medication is effective in 75% of people who have the disease. One hundred fifty individuals with Parkinson's disease are given the medication, and 100 of them note the medication was effective. Does this finding provide statistical evidence at the 0.05 level that the effectiveness is less than the 75% claim the company made? Make sure to include parameter, conditions, calculations, and a conclusion in your answer.

A clinical trial is planned to compare an experi- mental medication designed to lower blood pressure to a placebo. Before starting the trial, a pilot study is conducted involving 7 participants. The objective of the study is to assess how systolic blood pressure changes over time untreated. Systolic blood pres- sures are measured at baseline and again 4 weeks later. Is there a statistically significant difference in blood pressures over time? Run the test at a 5% level of significance. Baseline: 120 145 130 160 152 143 126 4 Weeks: 122 142 135 158 155 140 130

Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is which vaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 78 recipients of vaccine X and 93 recipients on vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 151. The vaccine Y recipients had a mean 6AEQ of y = 148. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is 0x = 8.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is dy = 11.5. The true (unknown) mean 6AEQ for vaccine X recipients is μx, while the true (unknown) mean 6AEQ for vaccine Y recipients is y. 6AEQ measurements are known to be a normally distributed. In summary: Type Sample Size Sample Mean Standard Deviation Vaccine X 78 Vaccine Y 93 151 148 8.7 11.5 a) Calculate the variance of the random variable X which is the mean of the 6AEQ measurements of the 78 vaccine X recipients.…

Suppose there are two different vaccines for Covid, Vaccine X and Vaccine Y. An interesting question is which vaccine has a higher 6-month antibody effectiveness quotient (6AEQ). To examine this we randomly select 78 recipients of vaccine X and 93 recipients on vaccine Y. The vaccine X recipients had a mean 6AEQ of x = 151. The vaccine Y recipients had a mean 6AEQ of y = 148. It is recognized that the true standard deviation of 6AEQ for vaccine X recipients is o, = 9.7 while it is recognized that the true standard deviation of 6AEQ for vaccine Y recipients is o, = 10.5. The true (unknown) mean SAEQ for vaccine X recipients is ly, while the true (unknown) mean 6AEQ for vaccine Y recipients is 4,. 6AEQ measurements are known to be a normally distributed. summary: Sample Size Sample Mean Standard Deviation 9.7 Гуре Vaccine 78 151 Vaccine Y 93 148 10.5 What is the length of your 96% confidence interval for uy Hy ? ) If we used this data to test Hg: Hy - Hy =0 against the alternative H: uy…

Find the a/2 ( the area in one tail outside of the confidence interval) and the critical value z a/2 necessary to construct an 80% confidence interval.