Question

Suppose it has previously been claimed that the proportion of adults in a certain region that have blood type O is 0.59 , and suppose we wish to carry out a test of the null hypothesis that this is the true proportion. In a random sample of 900 adults in this region, 564 have blood type O. What is the value of the appropriate Z test statistic? (Give your numeric response to at least 3 decimal places. Give only your numeric response, and not any extra characters or symbols. If the value is negative, include the negative sign) Suppose researchers are about to draw a sample of 1340 observations from a normally distributed population, and use this data to create a confidence interval for the population mean using the t procedure. They don't know much about statistics, and decide to use a t

α/2

value of 0.20 to calculate the margin of error. (Since, curiously, that is their favourite number.) What is the confidence level of this confidence interval? Express your response as a percentage, but do not include the percent sign. e.g. If the confidence level is 87.6%, then enter 87.6 . (Give your numeric response to at least 1 decimal place. Give only your numeric

Answer 1

Calculate the Z test statistic using the sample proportion, assumed population proportion, and standard error. Use the given t α/2 value to determine the confidence level for the t procedure.

Step-by-step explanation:

To find the Z test statistic for the given problem, we can use the formula:

Z = (p - μ) / σ

where p is the sample proportion (564/900), μ is the hypothesized population proportion (0.59), and σ is the standard error of the sample proportion, given by σ = √(p(1-p)/n). By plugging in the values, we calculate the Z test statistic.

For the second question regarding the confidence level for the t procedure, we'll reference the standard normal probability distribution. Using a t α/2 value of 0.20 implies that each tail of the distribution accounts for (1 - CL)/2. To find the confidence level (CL), we can use the formula CL = 1 - α.