# Correlation regression

**Topics:**Arithmetic mean, Statistical hypothesis testing, Profit

**Pages:**9 (2287 words)

**Published:**July 15, 2014

http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf (t table)

Critical Values (Z)Level of Significance

1%2%4%5%10%

Two Tailed±2.56±2.32±2.05±1.96±1.64

Right tailed+2.32+2.05+1.75+1.64+1.28

Left tailed-2.32-2.05-1.75-1.64-1.28

Q1) A cinema hall has cold drinks fountain supplying Orange and Ditzy Colas. When the machine is turned on, it fills a 550ml cup with 500ml of the required drink. The manager has three problems. I) The clients have been complaining that the machine supplies less than 500ml II) The manager wants to make sure that the amount of cola does not exceed 500ml III) The manager wants to minimize customer complaint and at the same time does not want any overflow. He takes up 36 cups of sample and finds the sample mean to be 499 ml. The specification of the machine says that generally the standard deviation is 1 ml. He does a hypothesis testing at 10% level of significance.

Q2) A tyre company wants to test the stress of tyres. The tyres should withstand a minimum load of 80,000kgs but excess load would burst the tyres. From the past experience, it is known that the standard deviation of the load is 4000kgs. A sample of 100 tyres was selected and tests were carried out. The result showed that mean stress capacity of the sample is 79,600 kgs. If the supplier uses a significance level of 5% in testing, do the tyres meet stress requirements? Also, find the limits of the acceptance region (or confidence limits).

Q3) A random sample of 400 flower stems has indicated that the average length of a stem is 10cm. Can this be regarded as a sample from a large population with a mean of 10.2cm and a standard deviation of 2.25cm at a significance level of 5%?

Q4) The height of 10 soldiers selected at random had a mean height of 158cm and variance of 39.06 cms. Assuming a significance level of 5%, test the hypothesis that the soldiers of the population are on the average lesser than 162.5 cms tall.

Q5) Business Today is conducting a survey between Sonepur and Muzaffarpur on the hourly wages of landless laborers. Results of the survey are as follows: TownMean Hourly wageS.DSample

SonepurRs8.95Rs0.40200

MuzaffarpurRs9.10Rs0.60175

Business Today wants to test the hypothesis at the 5% level of significance that there is no difference between hourly wages in the two towns.

Q6) The number of sales, average sales value and S.D of two sales team (one trained and the other not trained) are as follows:

Team A (Trained) Team B (Not Trained)

Sample sales1017

Avg sales value62005600

S.D690600

At a LOS 5%, find does training actually matter for generating sales value for the concerned company?

Q7) The Small Grocers Association is a group of independent grocers who have banded together so that they may compete with the larger supermarket chains. By making large purchases as a group, it is able to pay less than if it were to purchase as an individual store. Because of its new-found purchasing power, the Association wants to advertise that its prices are really lower than in supermarkets. It has chosen one product (1 kg potato) with which it plans to make its point in the advertisement. But before advertising and to check on this claim, the market research team obtained a random sample of prices from six Association Member Stores and nine supermarkets.

Q8) Hero Honda Ltd., as part of their operating policy, wished to determine whether there was a difference in customer satisfaction between the dealer’s customers and the company’s direct customers with respect to their warranty policies.

Q9) A company is contemplating to give VRS to its employees. The HR director tells the president that roughly 60% of the employees are eligible for VRS. The president forms a special committee to assess the eligible candidates. The committee conducts in-depth interviews with 120...

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