Statistics and Probability Answers

Paired T-Test and CI: WeightBeginning, WeightEnd

Paired T for WeightBeginning - WeightEnd

N Mean StDev SE Mean
WeightBeginning 20 64.74 5.99 1.34
WeightEnd 20 62.61 6.56 1.47
Difference 20 2.133 2.260 0.505


95% CI for mean difference: (1.075, 3.191)
T-Test of mean difference = 0 (vs ≠ 0): T-Value = 4.22 P-Value = 0.000

Research Question: On average, do adolescent females who take part in the “Get in Shape” programme experience a significant change in their body weights?

Hypothesis Test:

Include Diagrams when answering question
In 2014 the Department of Social Services reported that 32% of current marriages in Australia were expected to end in divorce.
Find the probability that more than 8 marriages out of a random sample of 20 marriages which were current in 2014 would end in divorce.

A Las Vegas roulette wheel has 38 different numerical values. If an individual bets on one number and wins, the payoff is 35 to 1.
a) Show a payoff table for a $10 bet on one number using decision alternatives of bet and do not bet.
b) What is the recommended decision using the expected value approach?

Two-sample T for LeanBodyMass

Sex N Mean StDev SE Mean
Male 75 52.63 6.66 0.77
Female 75 43.42 6.05 0.70

Difference = μ (Male) - μ (Female)
Estimate for difference: 9.21
95% CI for difference: (-, -)
T-Test of difference = 0 (vs ≠): T-Value = - P-Value = - DF = -
Both use Pooled StDev = 6.3633





Two-sample T for MetRate
SE
Sex N Mean StDev Mean
Male 75 1626 227 26
Female 75 1258 172 20

Difference = μ (Male) - μ (Female)
Estimate for difference: 367.9
95% CI for difference: (-, -)
T-Test of difference = 0 (vs ≠): T-Value = - P-Value = - DF = -
Both use Pooled StDev = 201.5088

b. Calculate a 95% confidence interval to estimate the difference between the average lean body mass of adolescent males and the lean body mass of adolescent females

Include an appropriate diagram for each part of this question

a. BranCrunch is a new breakfast cereal. Boxes of BranCrunch are labelled ‘ 675 grams’ but there is some variation. The actual mean weight is 675 grams with a standard deviation of 21 grams.
i. Dan’s Discount Store sells BranCrunch in mega-packs of 8 boxes. Assuming the weights of boxes of BranCrunch are normally distributed, find the probability that the average weight of a mega-pack of BranCrunch is higher than 665 grams.










ii. Louie’s Convenience Store receives a shipment of 30 boxes of BranCrunch. Louie’s will complain to the manufacturers if the total weight of this shipment is lower than 20 kg. Find the probability that Louie’s Convenience Store will complain about the shipment and explain why the information about the weights of BranCrunch following a normal distribution is not necessary to answer this part of the question.

Software filters rely heavily on “blacklists” (lists of known “phishing” URLs) to detect fraudulent e-mails. But such filters typically catch only 20 percent of phishing URLs. Jason receives 16 phishing e-mails.
What is the chance that such a filter would detect none of them?

The following probabilities for grades in management science have been determined based on past
records:
Grade Probability
A 0.1
B 0.2
C 0.4
D 0.2
F 0.10
1.00
The grades are assigned on a 4.0 scale, where an A is a 4.0, a B a 3.0, and so on. Determine the
expected grade and variance for the course.

The no. of defects in 20 pieces of cloth each of 100 meter length
is given below:
2, 1, 3, 3, 1, 6, 4, 3, 7, 10, 2, 2, 6, 4, 3, 2, 1, 5, 6, 4.
Draw the appropriate control chart and interpret the result.

in another experiment to see if getting candy after a meal would induce customers to leave a bigger tip a waitress randomly decided what to d with 80 dining parties. some parties received no candy some just one piece and some two pieces. others initially got just one piece of candy and than the waitress suggested that they take another piece. she recorded her tips received finding that in general the more candy the higher the tip but the highest tip (23%) came from parties who got one piece and than were offered more.

a) diagram this experiment
b)how many factors are there? how many levels?
c) how many treatments are there?
d) where is the response variable?
e) did this experiment involve blinding? double blinding?
f) in what way might have the waitress perhaps unintentionally have biased the results?

Researchers at the Washington University School of Medicine randomly placed 480 rats into one of three chambers containing radio antennas. one group was exposed to digital cell phone radio waves the second to analog cell phone waves and the third group to no waves. two years later the rats were examined for signs of brain tumors. in June 2002 the scientist said that differences among the three groups were not statistically significant.

a) is this a study or an experiment? explain
b)explain in this context what "not statistically significant" means.
c) comment on the fact that this research was funded by Motorola, a manufacturer of cell phones.