Question

.An industrial researcher is a consultant to a large chain of bookstores. Industry reports show that for book stores in general, the average number of complaints received by management for a 1-month period at this time of year is 6.5 (the variance is not known). 4 Seven of this chain’s stores are randomly selected to keep records of complaints received over a 1-month period. The numbers of complaints are 4, 8, 9, 0, 3, 5, and 6. Does this chain get a different amount of complaints than book stores in general? (Use the .05 level). what are the cut off values for a test with significance level 0.05?

test your hypotheses and state your conclusions

what is the effect size of the study

Answer 1

Here now the average number of the seven chain stroes complaints = (4 + 8 + 9 + 0 + 3 + 5 + 6)/7 = 5

Standard deviation of complaints = s = 3.055

standard error of sample mean = s/sqrt(n)= 3.055/sqrt(7) = 1.1547

Hypothesis are

null hypothesis : H₀ : = 6.5

Alternative Hypothesis : 6.5

Here degree of freedom dF = 7 - 1 = 6

t_critical = 2.447

so here test statistic

t = (5 - 6.5)/1.1547 = -1.3

here t < t_citical  so we will fail to reject the null hypothesis and we conclude that chain doesn'tget a different amount of complaints than book stores in general.

Here effect size = (M1 - M2)/s = (6.5 - 5)/3.055 = 0.49