Question

A 1990 Survey showed that the average check at Perkins family restaurant is $4.70. The Perkins company wants to know if this figure is too high for 1997. The Perkins company takes a random sample of 54 checks from the restaurants across the country and determines that the sample average check is $4.62. The sample standard deviation of the checks is $0.86. Using Alpha=0.05, test to determine whether the Perkins, restaurant check average is significantly lower than $4.70.

A. H0:
H1:

B. H0:
H1:

C.

Answer 1

	N	Mean	Std. Deviation	Std. Error Mean
1990	54	4.7	0.1	0.014
1997	54	4.62	0.86	0.117

Paired Samples Test
	Mean Difference	Std. Error Difference	t	df	Sig. (2-tailed)
Equal variances assumed	0.08	0.118	0.679	106	0.499
Equal variances not assumed	0.08	0.118	0.679	54.433	0.5
Hartley test for equal variance: F = 73.960, Sig. = 0.0000

H0: There is no significant difference in average check value at Perkins restaurant during the year 1990 and 1997 at 95% confidence interval

H1: There is significant difference in average check value at Perkins restaurant during the year 1990 and 1997 at 95% confidence interval

Interpretation:

The estimated Sig. value is 0.000 which is less than 0.05, this indicates the null hypothesis is rejected i.e. there is significant difference in average check value at Perkins restaurant during the year 1990 and 1997 at 95% confidence interval.

Or

Simply >

4.062 (+/-) 0.86 = 3.202 to 4.922 – A

4.70 (+/-) 0.05 = 4.2 to 4.75 – B

A doesn’t fall under the limit of B, so there is significant difference in value at 95% C.I.