An environmentalist estimates that the mean waste recycled b

An environmentalist estimates that the mean waste recycled by adults in the country is more than 1 lb per person per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of 15 adults in the country is 1.6 pounds and the standard deviation is 0.4 pound. At alpha=0.01, can you support the claim?

1. Find the critical value(s).

2. Find the standardized test statistic.

3. Decide whether to reject or fail to reject the null hypothesis.

4. Interpret the decision in the context of the original claim

Solution

Formulating the null and alternative hypotheses,          
          
Ho:   u   =   1
Ha:    u   >   1
          
As we can see, this is a    1   tailed test.  
          
Thus, getting the critical z,          
df =    14      
tcrit =    2.624494068 [part 1]
          
Getting the test statistic, as          
          
X = sample mean =    1.6      
uo = hypothesized mean =    1      
n = sample size =    15      
s = standard deviation =    0.4      
          
Thus, t = (X - uo) * sqrt(n) / s =    5.809475019 [part 2]
          
Also, the p value is          
          
p =    2.26385E-05      
          
Comparing z and zcrit (or, p and significance level), we   REJECT THE NULL HYPOTHESIS. [Part 3]

THERE IS SIGNIFICANT EVIDENCE AT 0.01 SIGNIFICANCE THAT THE MEAN WASTE RECYCLED PER PERSON PER DAY IS MORE THAN 1 LB PER PERSON PER DAY. [PART 4]