Statistics

Problem 1:

I am back in the lab, collecting samples.The mean of the sample is 75My associate wants to determine whether the sample meanstatistically greater than the population mean of 70. My associate set α = 0.05Please provide responses to:a- The probability associated with a mean of 75 is p = 0.05Can my associate reject the null hypothesis?b- If the null hypothesis is a correct statement,what is the probability that the researcher will makethe correct decision not to reject the null hypothesis?

Problem 2:

Use the following information to write the correspondingnull and alternative hypothesis:a-A sample mean of 23 is statistically differentr from apopulation mean of 30b- A sample mean of 56 is less than the population meanof 70c- A sample mean of 75 is greater than thepopulation mean of 70Be sure to show the relationship! Not just words.

Problem 3:

I have finished analyzing the data from a recent study.
There are 25 subjects in the sample
The mean of the sample is 75
The standard deviation is 4.7
Please answer the following:
a- What is the standard error o the mean for these data?
b- What are the 95% and 99% confidence intervals
c- What is the probability of obtaining by chance the following:
i - a mean less than 72
ii- a mean less than 74
iii- a mean greater than 76
iv- a mean greater than 78

Problem 4:

Two (2) students took the same statistics test.
Convert their scores to percentiles and plot on a chart.
You will need the z-table in the back of the text (or internet serach).
Math Test Results
X = 73.0
s = 8.0
John scores 79 on the test
Mary scored 68 on the test