Question

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

2. Answer Both Parts of the question

An industrial designer wants to determine the average amount of time it takes an adult to assemble an “easy to assemble” toy. A sample of 16 times yielded an average time of 19.92 minutes, with a sample 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 μ with α = 0.05, so that the error not exceeds 0.25?

3. Seven students got the following percentage of marks in Chemistry and Physics:

Student

                1              2              3              4              5              6              7

Marks in Chemistry         78           36           98           25           75           82           90

Marks in Physics               84           51           91           60           68           62           86

Calculate the correlation co-efficient for above data.

4. In a study between the amount of rainfall and the quantity of air 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

5. Find the coefficient of correlation for the following table:

x: 10       14           18           22           26          30

y: 18       12          24           6              30          36

Is the test statistics is significant using 5% level of significance?

Answer 1

Note allowed to solve one question per post. However solved two questions.

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

Hence we conclude that mean thermal efficiency of diesel engines produced by them is different from 32.3%

Seven students got the following percentage of marks in Chemistry and Physics:
Calculate the correlation co-efficient for above data.