Use the traditional method to test the given hypothesis. Assume that the populat

Question

Use the traditional method to test the given hypothesis. Assume that the population is normally distributed and that the sample has been randomly selected. 15) For randomly selected adults, IQ scores are normally distributed with a standard deviation of 15. The scores of 14 randomly selected college students are listed below. Use a 0.10 significance level to test the claim that the standard deviation of IQ scores of college students is less than 15. Round the sample standard deviation to three decimal places. 115 128 107 109 116 124 135 127 115 104 118 126 129 133

Explanation / Answer

15.

Using technology, the sample standard deviation is

s = 9.819245512

Formulating the null and alternative hypotheses,              
              
Ho:   sigma   >=   15  
Ha:    sigma   <   15  
              
As we can see, this is a    left   tailed test.      
              
Thus, getting the critical chi^2, as alpha =    0.1   ,      
alpha =    0.1          
df = N - 1 =    13          
chi^2 (crit) =    7.04150458        
              
Getting the test statistic, as              
s = sample standard deviation =    9.819245512          
sigmao = hypothesized standard deviation =    15          
n = sample size =    14          
              
              
Thus, chi^2 = (N - 1)(s/sigmao)^2 =    5.570793651          
              
              
As chi^2 < 7.042, then we REJECT THE NULL HYPOTHESIS.  

Hence, there is significant evidence at 0.10 level that the standard deviation of IQ scores of college students is less than 15. [CONCLUSION]          

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.