Question

Over the past year, the number of riders (X) of a local bus route varied with a mean daily ridership of 956.3 and a standard deviation of 18.7.

Use the above preamble to answer the following

i) If samples of size n = 100 days are to be taken from the past year, describe the sampling distribution of the sample mean for these samples of size n = 100 days. Is the sampling distribution normally distributed?

ii) If samples of size n = 20 days are to be taken from the past year, describe the sampling distribution of the sample mean for samples of size n = 20 days. Is the sampling distribution normally distributed?

iii) What must be true about the population of daily ridership levels in order for what you said in i) to be permissible in ii)?

iv) What specific (other) name is given to the standard deviation of a sampling distribution?

Answer 1

X = No of riders of a local bus route E(x) = 956 3=4 , &- 18.7 CLT says, irrespective of population dist are lid, as lu, 2/n) (il n=100 ü large =) XaN(956.3). if observations for large n. а пти Сам (ii) n = 20 is small 50, deviations will targer but if we take more & noxe samples, 7 ~ N(956.3, (18.73²) 20 isrespective of u if, more somples are generated, 7 & N(4, 6/n) iii) observations should be identically & independently distributed il. No of riders should not be dependent on previous days () sine , we are dealing with sample, so. standard error term should be used instead standard deviation