1. A company claims that the mean thermal efficiency of dieselengines produced by them is 32.3%. To test this, claim a randomsample of 40 engines were examined which showed the mean thermalefficiency of 31.4% and standard deviation of 1.6%. Can the claimbe accepted at 1% level of significance?

1. Answer Both Parts of the question

An industrial designer wants to determine the average amount oftime it takes an adult to assemble an “easy to assemble” toy. Asample of 16 times yielded an average time of 19.92 minutes, with asample standard deviation of 5.73 minutes. Evaluate a 95%confidence interval for the mean assembly time.

How large should a sample be to estimate the population mean μwith α = 0.05, so that the error not exceeds 0.25?

1. Seven students got the following percentage of marks inChemistry and Physics:

Student

               1             2             3             4             5             6             7

Marks inChemistry        78          36          98          25          75          82          90

Marks inPhysics              84          51          91          60          68          62          86

Calculate the correlation co-efficient for above data.

1. In a study between the amount of rainfall and the quantity ofair pollution removed, the in following data were collected

               

Daily rainfall (x)

(in 0.01 cm)       1.53       1.78       2.60       2.95        3.42

Pollution removed (y) (mg/ m3) 33.50    36.30    40          45.80     53.50

Obtain the line of regression of y on x from the above data.Compute y when x = 3.55

1. Find the coefficient of correlation for the followingtable:

x: 10      14          18          22          26          30

y: 18      12         24          6             30          36

Is the test statistics is significant using 5% level ofsignificance?