Question

Rainy Weekends - Significance Test: During the summer of 2012 in Acadia National Park, the mean rainfall on weekends was greater than the mean on weekdays. In this problem we determine whether or not it rained significantly more on weekends. A significant difference is one that is unlikely to be a result of random variation. The table summarizes this data. The

x

's are actually population means but we treat them like sample means.

Necessary information:

	n	x	s2	s
Weekends (x1)	36	0.298	0.283	0.532
Weekdays (x2)	89	0.116	0.284	0.533

The Test: Test the claim that the mean amount of rain on weekends was significantly greater than weekdays. Use a 0.01 significance level.

(a) Calculate the test statistic using software or the formula below.t =

(x1 − x2) − δ

s12 n1 + s22 n2

where δ is the hypothesized difference in means from the null hypothesis. Round your answer to 2 decimal places.
t =  
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.  

(b) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =  

(c) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀     

(d) Choose the appropriate concluding statement.

The data supports the claim that the mean amount of rain on weekends was significantly greater than weekdays.

While it did, on average, rain more on weekends, the difference was not great enough to be considered significant.       

We have proven that something was making it rain more on weekends than on weekdays.

We have proven there was no difference between the mean amount of rain on weekends and weekdays.

Answer 1

Solution:

We are given

	n	x	s2	s
Weekends (x1)	36	0.298	0.283	0.532
Weekdays (x2)	89	0.116	0.284	0.533

(a) Calculate the test statistic using software or the formula below:

Two sample t test for mean assuming unequal population variances

t = (X1bar – X2bar) / sqrt[(S₁² / n₁)+(S₂² / n₂)]

t = (0.298 – 0.116)/sqrt[(0.283/36)+(0.284/89)]

t = 0.182/ 0.1051

t = 1.7311

Test statistic = t = 1.73

(b) Use software to get the P-value of the test statistic.

P-value = 0.0441

(by using excel)

(c) What is the conclusion regarding the null hypothesis?

We are given

α = 0.01

P-value = 0.0441

P-value > α

So, we fail to reject H₀

Answer: Fail to reject H₀

(d) Choose the appropriate concluding statement.

Answer:

We have proven there was no difference between the mean amount of rain on weekends and weekdays.