A consumer products company is formulating a new shampoo and

A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wished to test H₀: = 175 against H₁: > 175 millimeters, using the results of n =10 samples.

1) If the sample data result in = 190 millimeters, find the value for the test statistic z₀.

Round the final answer to two decimal places (e.g. 98.76)

2)How \"unusual\" is the sample value = 190 if the true mean is really 175? That is, what is the probability you would observe a sample average as large as 190 millimeters (or larger), if the true mean foam height was really 175 millimeters?  

Solution

1.

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   175  
Ha:    u   >   175  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    190          
uo = hypothesized mean =    175          
n = sample size =    10          
s = standard deviation =    20          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.37 [ANSWER]

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2)

Using table/technology, the right tailed area of this z score is
          
p =    0.008853033   [ANSWER]