Question

A survey of 192 medical school interns, whose results were published in the New England Journal of Medicine in January 2005, found them to average 57 hours of work a week, with standard deviation of 16 hours.

(a) Explain why the distribution of sample mean, x, will have an approximate normal shape even if the distribution of hours worked is not normal.

The standard deviation is large.

The sample size is small.     

The standard deviation is small.

The sample size is large.

(b) Explain why standardized sample mean will follow an approximate z distribution, even if we standardize with sample standard deviation s instead of population standard deviation σ.

For a small sample s is close to μ.

For a small sample s is close to σ.     

For a large sample s is close to μ.

For a large sample s is close to σ.

(c) Report an approximate 95% confidence interval for mean hours worked per week by the population of interns, rounding to the nearest tenth (one decimal place).
(  ,  )

(d) Which procedure would we use if the interval were to be constructed with software?

a t procedure

a z procedure     

(e) Explain why 40 is not a plausible value for population mean hours worked per week, based on your confidence interval.

40 falls above the interval.

40 falls below the interval.     

40 falls within the interval.

(f) If population mean equaled 40, find the value of the standardized sample mean. (Round your answer to two decimal places.)


(g) Explain why 40 is not a plausible value for the population mean hours worked per week if sample mean is 57, based on the standardized value of 57.

The sample size is too large.The standard deviation is too large.     

The standardized sample mean would be too small to be believable.

The standardized sample mean would be too large to be believable.

(h) If we were to carry out a formal test to see if the population mean could be 40, based on a sample mean of 57, how should the alternative hypothesis be written?

H_a: x ≠ 40

H_a: μ ≠ 40     

H_a: x > 40

H_a: μ > 57

H_a: μ ≠ 57

(i) Based on your confidence interval in part (c), would you reject the null hypothesis in favor of the alternative?

Yes

No    

Answer 1