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Statistics and Probability Answers

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The manager of the supermarket thinks that the probability of a person buying a gigantic chocolate bar is only 0.02 to test whether this hypothesis is true the manager decides to take a random sample of 200 people who bought bars.
1) find the critical region that would enable the manager to test whether or not there is evidence that the probability is difficult from 0.02. the probability of each tail should be as close to 2.5 % as possible.
2) write down the significance level of this test
Past records from a large supermarket show that 20% of people who buy chocolate bars buy the family size bars. On one particular day a random sample of 30 people was taken from those that had bought chocolate bars and 2 of them were found to have bought a family size bar.
1) test at the 5 % significance level, whether or not the proportion of people who bought a family size bar of chocolate that day had decreased. State your hypothesis clearly.
A new diet program claims that participants will lose an average at least eight pounds during the week of the program. a random sample of 40 people participating in the program showed a sample mean weight loss of seven pounds. the sample standard deviation was 3.2 pound.
1) what is the rejection rule with a=0.05
2) What is your conclusion about the claim made by the diet program
3) what is the p-value
A tennis coach believes that taller players are generally capable of letting faster serves. to investigate this hypothesis he collects data on 20 adult male players he coaches. The height h,in a matter and the speed of each player faster serve,v in km per hour were recorded and summarized as follows
h=36.22
v=2275
h2=65.7396
V2=259853
HV=4128.03
Calculate the pearson moment correlation coefficient for these data
2. comment on the which hypothesis
A consumer group claims that more than 62% of people choose coffee rather than other beverages as their preferred drink in the morning. In the sample of 92 people, 68 reported that they prefer coffee. At α = 0.03, is there enough evidence to support the consumer group’s claim?
A sample of 100 motorcar types has a mean of 20,000km and a standard deviation of 800km. as second sample of 150 tyres has amean life of 22,000km and a standard deviation of 900km
1. is it true to say that the two samples were drawn from the population?
2. whic is your rejection or acceptance as you conclude about the two population
A child welfare officer assets that the mean sleep of young babies is 4 hours a day. A random sample of 64 babies show that their mean sleep was only 13 hours 30 minutes with a standard deviation of 3 hours. at 5 % level of significance ,test the assertion that mean sleep of babies is less than 14 hours a day
1.WHAT IS TIME SERIES ANALYSIS

2. WHAT IS THE MOVING AVERAGES SYSTEM OF FORECASTING
WEEK 1 2 3 4 5 6 7 8

NO OF BAGS 340 330 323 343 350 345 365 324
CALCULATE THREE WEEK MOVING AVERAGES AND SIX WEEKS MOVING AVERAGES

the lifetime of a car batteries is normally distributed with mean 1 year and standard deviation 1.5 months
a)calculate the probabilty that a randomly selected car battery will last 10 to 11 months
b)calculate the minimum lifetime of the 30% longest lasting car batteries
c) by improing the quality of the car batteries, the lifetime is to be increased such that only 2.5% of the car batteries will fail before 10 months.Find the new mean lifetime of the car batteries, Assume the standard deviation remains unchanged,
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