Measurements of the weights of a random sample of 200 ball bearings made by certain machine during one week showed a mean of 0.824 newtons and a S.D. of 0.042 newton's. Find
a) 95% and
b) 99% confidence limits for the mean weight of all the ball bearings.

A sample poll of 100 voters chosen at random from all voters in a given district indicated that 55% of them were in favour of a particular candidate. Find
(a) 95% confidence limits
(b) 99% confidence limits for the proportion to all voters in favour of this candidate.

The mean breaking strength of cables supplied by a manufactures is 1900 \(\frac{n}{m^{2}}\) with a standard deviation of \(\frac{n}{m^{2}}\). The manufacture introduced a new technique in the manufacturing process and claimed that the breaking strength of cables has increased. In order to test the claim, a sample of 60 cables is tested. It is found that the mean breaking strength of the samplcd cables is \(1960 \frac{n}{m^{2}}\). Can we support the claimn at 1% level of significance.

A motor vehicle company desires to introduce a new model vehicle. The company claims that the mean fuel consumption of its new model is lower than that of the existing one which is 27 kms/litre. A sample of 100 vehicles of the new model is sclected and their fuel consumption are observed as 30 kms/litre with a standard deviation off 3 kms/litre. Test the claim of the company at 5% level of significance

A company producing LED bulbs finds that the mean life spar of the population of the bulbs is 2000 hours with a standard deviation of 150 hours. A sample of 100 bulbs is found to have the mean life spar of 1950 hours. Test at 5% level of significance wheather the mean life spar of the bulbs is significantly different from 2000 hours.

A survey was conduced among the citizens of a city to study the preference towards consumption of tea and coffee. Among 1000 randomly selected persons, it is found that 560 are tea drinkers and remaining coffee. Can we conclude at 1%. Level of significance from the information that both tea and coffee are equally preferred among the citizens in the city.

Measurements of the weights of a random sample of 200 ball bearings made by a certain machine during one weck showed a mean of 0.824 newtons and a standard deviation of 0.042 newtons. Find
(a) 95% and
(b) 99 confidence limits for the mean weight of all the bell bearings.

A sample poll of 100 voters chosen at random from all voters in a given district indicated that 55% of them were in favour of a particular candidate.
(a) 95% confidence limits
(b) 99% confidence limits for the proportion of all voters in favour of their candidate

The mean life time of 50 electric bulbs produced by a manufacturing company is estimated to be 825 hours with a standard deviation of 110 hours. If \(\mu\) in the mean life time of all the bulbs produced by the company, test the hypothesis that \(\mu\) = 900 at 5% level of significance.

A company markets car tyres. Their lives are normally distributed with a mean of 50000 kms and standard deviation of 2000 kms. A test sample of 64 tyres has a mean life of 51250 kms. Can you conclude that the sample mean differs significantly from the population mean (Test at 5% level)

The income distributor of the population of a village has a mean of Rs. 6000 and a variance of Rs. 32,400 could a sample of 64 persons with a mean income of Rs. 5950 belong to this population (Test at both 5% and 1% level of significance)

A sample of 400 students is found to have a mean height of 171.38 cms. Can it reasonably be regarded as a sample from a large population with mean height of 171.17 cms and standard deviation of 3.3 cms (Test at 5% level)

The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with mean IQ 100 and standard deviation 15. (Test at 5% leve of significance)

To test the conjecture of the management that 60 percent employees favour a new bonus scheme a sample of 150 employees was drawn and their opinion was taken whether they favoured it or not. Only 55 employces out of 150 favoured the new bonus scheme (Test at 1% level of significance).