Statistics and Probability Answers

A standard test given to a large number of student had a mean of 74 with a standard deviation of 8.
Find the percentage of students who scored
a. between 72 and 80
b. between 68 and 76
c. more than 76

A survey of college students collected information on several variables: Distance formhome, Age, Major, Gender, and Class. The variable Major is

Two persons agreed to meet at a certain place between 2 PM and 3 PM. Each person has to wait another one for 10 minutes and then leave. What is the probability of their meeting if everyone can arrive whenever during this hour?

Do a two sample t test. Assume that this is a two sided test with alpha 5%.
Find the test stat, p-value and make a decision about the null.

A researcher hypothesized that the pulse rates of long-distance athletes differ from those of other athletes. He believed that the runners’ pulses would be slower. He obtained a random sample of 10 long-distance runners. He measured their resting pulses. Their pulses were 45, 45, 64, 50, 58, 49, 47, 55, 50, 52 beats per minute. The average resting pulse of athletes in the general population is normally distributed with a pulse rate of 60 beats per minute.
a. What statistical test should be used to analyze the data?

A coffeehouse wishes to see whether customers have any preference among five different roasts of coffee.& A sample of 200 customers provided the data shown in the table below.& Test the claim that the customers do not have a preference for one type of roast over another.& Use level of significance.

Coffee:
Type of Roast& & & & & & & Number of Customers
(Preferring this Roast over Others)
“Eye Opener”& & & & & & & & & 37
“Dragons Breath”& & & & & 38
“Mediocre Medium”& & 52
“Decaf Ennui”& & & & & & & & & & & & 45
“Hazelnut Heaven”& & & & & 28

a)& & & State the null and alternative hypotheses.
b)& & & Find the critical value(s) and sketch the rejection region.
c)& & & Find the test statistic.
d)& & & Circle one:& & & & Reject Ho& & & or& & & Do not Reject Ho
e)& & & State the conclusion in terms of the described study.&

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What does central limit theorem mean.

A class had 20 A’s, 8 B’s, 7 C’s, 1 D and 3 F’s. The median score received what letter grade?

A researcher looks at old medical records for cancer patients to compare treatments and recovery rates. Is this an experiment or observational study? Explain.