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.
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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 |
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.
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 |
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.
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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If the magnitude of the earthquakes recorded in a region of a country follows a distribution with parameter θ
then find
i) maximum likelihood estimator of the parameter θ,
ii) maximum likelihood estimate of the parameter on the basis of the following data:
| Magnitude of the Earthquakes (on the Richter scale) |
6.7 |
7.7 |
5.6 |
7.3 |
6.7 |
6.6 |
7.8 |
6.7 |
6.2 |
5.2 |
State whether the following statements are True or False. Give reason in support of your answer:
(a) If the probability density function of a random variable X follows F-distribution is
then degrees of freedom of the distribution will be (2,2).
(b) The number of runs in the sequence HTTTHTHTTTHT will be 6.
(c) A patient suffering from fever reaches to a doctor and suppose the doctor formulate the hypotheses as H0 : The patient is a chikunguniya patient H1 : The patient is not a chikunguniya patient If the doctor rejects H0 when the patient is actually a chikunguniya patient, then the doctor commits type II error.
(d) In a random sample of 525 families owning television set in the region of New Delhi, it is found that 370 subscribe to Star Plus. A 95% confidence interval for the actual proportion of such families in New Delhi which subscribe to Star Plus will be (0.66, 0.74).
(e) For testing the pulse rate of one month old child is to be 120 per minute, a researcher measures (per minute) the pulse rate of 10 one month old children and applies sign test and Wilcoxon signed-rank test, then power of the Wilcoxon signed-rank test is more than the sign test.