Question

Dominick Aldo owns and operates Carolina’s which is an Italian restaurant in New York. The file Single Population.xlsx is shown below and contains the amount of time that table times varied from table to table.

A) Test the hypothesis that the average table time exceeds 98 minutes using 0.05 ? = . B) What is the p-value? Interpret the results.

Be sure that your project shows the following steps 1. Null and alternative hypothesis 2. Determine which distribution to use for the test statistic. 3. Using data provided, calculate necessary sample statistics. 4. Draw a conclusion and interpret the decision.


Time 70 80 100 90 75 60 70 75 110 90 100 75 60 75 80 75 165 60 75 90 110 95 110 150 50 70 90 110 165 60 145 80 115 75 50 90 110 90 100 110 110 85 70 145 120 130 80 90 105 105 100 95 80 100 120 130 75 90 70 125 80 90 95 120 150 195 70 80 110 80 80 85 90 150 60 90 135 170 85 90 120 105 60 70 50 80 100 90 135 120

Answer 1

1. Null and alternative hypothesis

Null Hypothesis:

H0:mu=98

Alternative Hypothesis:

H1:mu>98

Determine which distribution to use for the test statistic.

normal distribution since sample szie n=90 which is n>30 ,use t statistic since population deviation is not known.

Solution3:

n=90

population mean=98

sample mean=96.77778

sample standard deviation=s=29.10955

critical value=1.662,

standard error of mean=s/sqrt(n)

=29.10955/sqrt(90)

standard error of mean=3.068

level of significance=0.05

t=sample mean-population mean/sample sd/sqrtn)

=96.77778-98/29.10955/sqrt(90)

t=-0.39832

degrees of freedom=n-1=90-1=89

4. Draw a conclusion and interpret the decision.
p=0.6543

p>0.05

Do not reject Null hypothesis.

Accept null hypothesis.

Conclusion:

there is no sufficient evidence at 5% level of significance to support the claim that the average table time exceeds 98 minutes .

Code in R:

time <- c(70, 80, 100 ,90, 75, 60, 70, 75, 110, 90,

100, 75, 60, 75 ,80 ,75, 165, 60, 75, 90,

110, 95, 110, 150, 50, 70, 90, 110, 165, 60,

145, 80 ,115, 75, 50, 90, 110, 90, 100, 110 ,

110, 85 ,70 ,145, 120, 130 ,80, 90, 105, 105 ,

100, 95, 80, 100, 120, 130, 75, 90, 70, 125 ,

80, 90, 95, 120, 150, 195 ,70, 80, 110, 80, 80,

85, 90, 150 ,60, 90, 135, 170, 85, 90, 120, 105 ,

60, 70 ,50 ,80, 100 ,90 ,135, 120)

t.test(time,mu=98,alternative ="greater" )

output:

One Sample t-test

data: time
t = -0.39832, df = 89, p-value = 0.6543
alternative hypothesis: true mean is greater than 98
95 percent confidence interval:
91.67759 Inf
sample estimates:
mean of x
96.77778

t=-0.39832

p= 0.6543

p>0.05

Do not reject H0.