Question

Heights were measured for a random sample of 10 plants grown while being treated with a particular nutrient. The sample mean and sample standard deviation of those height measurements were 31 centimeters and 12 centimeters, respectively. Assume that the population of heights of treated plants is normally distributed with mean J. Based on the sample, can it be concluded that ju is different from 42 centimeters? Use the 0.05 level of significance. Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table The null hypothesis: H o P x s The alternative hypothesis: dº Did 00 OS The type of test statistics (Choose one) DO DO > The value of the test statistica (Round to at least three decimal places.) 0 X 5 The two critical values at the 0.05 level of significance (Round to at least three decimal aces and I Continue Set Assim

Answer 1

Ho :   µ =   42  

Ha :   µ ╪   42  

TYPE OF TEST : T TEST
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    12.0000  
Sample Size ,   n =    10  
Sample Mean,    x̅ =   31.0000  
          
degree of freedom=   DF=n-1=   9  
          
Standard Error , SE = s/√n =   12/√10=   3.7947  
t-test statistic= (x̅ - µ )/SE =    (31-42)/3.7947=   -2.899  
          
critical t value, t* =    -2.2622 ,2.2622 [Excel formula =t.inv(α/no. of tails,df) ]

|TETS STAT| > |CRITICAL VALUE | , REJECT Ho

yes, mean height is different than 42

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