1. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, p-value, critical value(s), and state the final conclusion that addresses the original claim.
– In a manual on how to have a number one song, it is stated that a song must be no longer to of 227.6 seconds and a standard deviation of 55.36 seconds. Use a 0.05 significance level and the accompanying minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 seconds. What do these results suggest about the advice given in the manual?
Test of mu=210 vs >210
Mean = 227.60
St dev= 55.36
Se mean= 8.75
95% lower bound = 212.85
2. A simple random sample of 59 adults is obtained from a normally distributed population, and each persons red blood cell count ( in cells per microliter) is measured. This sample mean is 5.25 and the sample standard deviation is 0.53. Use a 0.01 significance level and given calculator display to test the claim that the sample is from a population with a mean less than 5.4, which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample group?
a. Identify the null and alternative hypotheses
b. Identify the statistic that is relevant to the test (type interger or decimal)
c. Identify the test statistic (round 3 decimal places)
d. Identify the p value (round 4 decimal places)
e. Find the critical values (left tailed,right or double)(round 3 decimal places)
3. For the following claim, find the null and alternative hypotheses, test statistic, p-value, critical value, and draw a conclusion. Assume that a simple random sample has been selected from a normally distributed population.
Claim: the mean IQ score of statistics professors is greater than 129.
Sample data: n=16
Significance level is a = 0.05