Question

In a random sample of 9 cell​ phones, the mean full retail price was ​$522.20 and the standard deviation was ​$191.00. Further research suggests that the population mean is ​$425.49. Does the​ t-value for the original sample fall between -t 0.95 and t 0.95​? Assume that the population of full retail prices for cell phones is normally distributed. The​ t-value of t=____ does does not??? fall between -t 0.95 and t 0.95 because t 0.95=___ ​(Round to two decimal places as​ needed.)

Answer 1

SOLUTION:

From given data,

In a random sample of 9 cell​ phones, the mean full retail price was ​$522.20 and the standard deviation was ​$191.00. Further research suggests that the population mean is ​$425.49. Does the​ t-value for the original sample fall between -t _0.95 and t _0.95 .

Sample size = = 9

mean = =  425.49

Sample mean =   = 522.20

Standard deviation = = 191.00

Degrees of freedom = n - 1 = 9 - 1 = 8

Confidence level = 0.95

= 1 - Confidence level

= 1 - 0.95

= 0.05

Critical value

-t_0.05,8 = -2.306

t_0.05,8   = 2.306

t-test statistic is

t = - / ( / )

=  522.20 - 425.49 / ( 191.00 / )

   = 96.71 / 67.528697

= 1.4321318

The t-value of t = 1.43 does fall between -t _0.95 and t _0.95 because t _0.95