Question

The time to process hot-rolled steel has a standard deviation of 0.9 minutes. A sample of size 30 is selected which has an average of 5.5 minutes.

(a) Find a 99% confidence interval for the mean time to process hot-rolled steel.

(b) Find a 95% confidence interval for the mean time to process hot-rolled steel.

(c) Find a 90% confidence interval for the mean time to process hot-rolled steel.

(d) What happens to the confidence interval as α significance level decreases? Explain.

Answer 1

Solution-;

Given:

(a) To find 99% C.I. for the mean ti,e process hot-rolled steel, at

Where, (From t-table)

The required 99% C.I. for the mean ti,e process hot-rolled steel is

(b) To find 95% C.I. for the mean ti,e process hot-rolled steel, at

Where, (From t-table)

The required 95% C.I. for the mean ti,e process hot-rolled steel is

(c) To find 90% C.I. for the mean ti,e process hot-rolled steel, at

Where, (From t-table)

The required 90% C.I. for the mean ti,e process hot-rolled steel is

(d)     

  

  

From above three C.I. we seen that α significance level decreases then in Confidence Interval lower limit increses and upper limit drecreases. Also width of C.I. decreases.