An engineer conducted an experiment to compare two metals: iron and copper, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the breaking pressures are given in the following table:
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S. No. | Breaking Pressure | |
| Iron | Copper | |
| 1 | 72.7 | 73 |
| 2 | 69.6 | 67.2 |
| 3 | 83.4 | 75.3 |
| 4 | 78.9 | 61.4 |
| 5 | 75 | 74 |
| 6 | 71.6 | 69.5 |
| 7 | 85.7 | 69.8 |
| 8 | 73.5 | 73.8 |
| 9 | 70.4 | 68 |
| 10 | 84.2 | 76.1 |
If the breaking pressures for both iron and copper are normally distributed, are the variances of the distributions of the breaking pressure of iron and copper equal at 5 % level of significance?
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An ambulance agency claims that the mean length of service times is 10 minutes. Investigator suspects that this claim is wrong. She takes a random sample of 20 services and finds the mean length of service times is 15 minutes. Assume that the service time of the ambulance follows normal distribution.
i) What is the probability that the mean length of service times is more than and equal to 10 minutes.
ii) Find the 95% confidence interval for the standard deviation of the mean length of service times.
Complete the following table, one is done for you:
| S. No. | Test For | Name of the Test | Test Statistic | Assumptions for Applying the Test | Test Type |
| 1 | Population mean when population variance is known and population is normal | Z-test | 1. Sample observations should be independent. 2. The measurement scale should be at least interval scale. | Parametric Test | |
| 2 | Population mean when population variance is unknown and population is normal |
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| 3 | Population mean/median when the form of population is not known and sample size is small |
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| 4 | Population mean/median when the form of population is not known and the data is in ordinal scale and sample |
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| size is small |
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| 5 | Population variance when the population is normal distributed and sample size is small |
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| 6 | Independence of Two Attributes |
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The lifespan (in ‘000 hours) of five LED bulbs of 07 watts are as follows: 40, 46, 48, 50, 42
(i) How many samples of size 2 are possible without replacement? Write them.
(ii) Compute mean of all samples of size 2 and set up the sampling distribution of the sample mean.
(iii)Compute the expected value and standard error of the sample mean.
A sample of 500 shops was selected in a large metropolitan area to determine various information concerning the consumer behaviour. One question, among the questions, asked, was “Do you enjoy shopping for clothing?” Out of 240 males,136 answered yes. Out of 260 females, 224 answered yes. Find 95% confidence interval for the difference of the proportions for enjoys shopping for clothing.
An engineer conducted an experiment to compare two metals: iron and copper, as bonding agents for an alloy material. Components of the alloy were bonded using the metals as bonding agents, and the pressures required to break the bonds were measured. The data for the breaking pressures are given in the following table:
|
S. No. | Breaking Pressure | |
| Iron | Copper | |
| 1 | 72.7 | 73 |
| 2 | 69.6 | 67.2 |
| 3 | 83.4 | 75.3 |
| 4 | 78.9 | 61.4 |
| 5 | 75 | 74 |
| 6 | 71.6 | 69.5 |
| 7 | 85.7 | 69.8 |
| 8 | 73.5 | 73.8 |
| 9 | 70.4 | 68 |
| 10 | 84.2 | 76.1 |
To study whether or not the level of earning is affected by educational attainment, a social scientist randomly selected 100 people from each of three income categories ‘low’, middle’,
‘high’ and then recorded their educational attainment as in the following table:
| Educational attainment | Income Categories | Total | ||
| Low | Middle | High | ||
| No college UG PG Doctoral | 32 13 43 12 | 20 16 51 13 | 23 1 60 15 | 75 30 154 41 |
| Total | 100 | 100 | 100 | 300 |
Results of a survey by the National Centre for Health Statistics indicated that people between 65 and 74 years of age contact a physician an average of 9.8 times per year. People 75 and older contact physicians an average of 12.9 times per year. Suppose you want to validate these results by taking your own samples and obtained the following data represent the number of annual contacts people make with a physician. The samples are independent.
| Number of annual contacts people make with a physician | |
| 65 to 74 | 75 and Older |
| 12
13 | 16
15 |
| 8 11 9 6 11 | 10 17 13 12 14 9 13 |