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The manufacturer of a patent medicine claimed that it is effective in relieving 90% of the


people suffering from the disease. From a sample of 200 people using the medicine 160


were relived of suffering. Determine if the claim is legitimate.


21) In 324 throws of a six face die odd points appeared 181 times. Would you say that the die


is ‘fair’? State the level of significance, you use.


22) In a random sample of 400 persons taken from a large population 120 were females. Can


it be said that male and females are in the ration 5:3 in the population. Use 1% level of


significance.

The mean breaking strength of cables supplied by a manufacturer is 1800 with standard


deviation 100. By a new technique in the manufacturing process, it is claimed that the


breaking strength of the cable has increased. In order to test the claim a sample of 50 cables


is tested. It is found that the mean breaking strength is 1850. Can we support the claim at


1% level of significance?


19) A coin is tossed 400 times and was found to result in head 245 times. Can we conclude the


coin is fair?

A machine is claimed to produce nails of mean length 5cm. and standard deviation of


0.45cm. A random sample of 100 nails gave 5.1cm. as their average length. Does the


performance of the machine justify the claim? Mention the level of significance you apply?


16) The mean height of random sample of 100 individuals from a population is 160 cms. The


S.D. of the sample is 10cms. Would it be reasonable to suppose that the mean height of the


population is 165cms?


17) A sample of 50 pieces of certain type of string was tested. The mean breaking strength


turned out to be 14.5 gms. Test whether the sample is from a batch of a string having a


mean breaking strength of 15.6 gms and standard deviation of 2.2 gms.

A survey was taken of 800 randomly selected students asking them if they used public transportation to get to class. 120 answered that they did. Construct a 95% confidence interval for this proportion.


1. Please take a piece of paper and write down the process of establishing confidence interval step by step.

2. According to past experience, 20% of students took public transportation. Test if the situation changed. Solve the problem step by step.


A real estate agent has compiled some data on the selling prices of recently sold homes (in $10 000) compared to their distance from the nearest school (in km). Distance From School (km) 8 7 9 10 4 11 2 11 1 2 12 5 9 8 3 1 6 Selling Price ($ 10 000) 20 17 9 25 10 5 6 31 31 29 2 18 23 12 24 2 15 The real estate agent runs a linear correlation and concludes that, with a correlation coefficient of 𝒓 ≐ −𝟎. 𝟏𝟎, there is no relationship between the distance from a school, and the selling price. Is this completely true? Comment on the validity of his result and provide an explanation for the result. (Hint: Look at a scatter plot of the data. It is not necessary to draw the scatter plot on your paper.) 


The manufacturer of a new drug claims that it will lower

blood pressure by 13 points on the average. When the drug was

administered to 6 patients, the following drops in blood pressure

were registered: 12, 8, 15, 9, 10 and 16. Is the claim sustained at

the 0.05 level of significance.


From the past experience, a prof knows that the test score of a student taking his final xm is a random variable with mean 75 and variance 25.what os can be said about the probability that a student will score between 65 and 85.

A sample random sample of size 4 is drown with replacement from a population with s.d. 6 what is the S. E of the sample mean?

You are the Manager of a new computer manufacturing company, Fongkomputer. Tests have shown that the mean life time of your computers is normally distributed, and on average your computers last for only 9 months, with a standard deviation of 3 months. The managing director wants the chance of computer being returned within its guarantee period to be 10%. Suggest a guarantee period that will achieve this objective. Round your solution to the nearest month


Using thye following information: H0:=375; Ha: 375; n=100; x = 390; 2=4,900 and a =0.05. is the z-test statistic value equal to 2.14?


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