Question

PROBLEM 1: A random sample of 64 bags of corn flakes weigh, on average, 5.23 ounces with a standard deviation of 0.24 ounces. The manufacturer wants to put on the label that the average weight is 5.5 ounces. Test the hypothesis that μ≥.5.5 ounces against the alternative hypothesis, μ <5.5 ounces with a level of significance of 0.05. POSSIBLE ANSWERS: a) z = -9 is not rejected Ho b) z = -2 is not rejected Ho c) z = -2 rejects Ho d) z = -9 is rejected Ho

PROBLEM 2: An electric company manufactures cell batteries that have a duration that is distributed approximately normally with an average of 800 hours and a standard deviation of 40 hours. If a random sample of 30 batteries has an average duration of 788 hours, do the data show enough evidence to say that the average duration is not 800? Use a level of significance of 0.04. POSSIBLE ANSWERS: a) z = -1.643 Ho is rejected b) t = -1.643 is rejected Ho c) z = -1.643not RHo d) t = -1.643 not rejected Ho

PROBLEM 3: One school argues that the average weight of the students is 68 kg. It is known from experience that the standard deviation is 3.6 kg. To test the hypothesis of the school, an inspector of the Ministry of Education takes a sample of 36 students and decides to reject the school's affirmation if the average of the sample is less than 67 kg or greater than 69 kg. Calculate the alpha and beta values corresponding to the previous statement. (To obtain the value of beta, suppose that later it is verified that the true average is 70 kg). POSSIBLE ANSWERS: a) alpha = 0.9 beta = 0.1 b) alpha = 0.015 beta = 0.085 c) alpha = 0.095 beta = 0.0475 d) alpha = 0.5 beta = 0.499

PROBLEM 4: A random sample of 100 deaths registered in the United States last year shows an average life of 71.8 years. Assume a population standard deviation of 8.9 years. We want to test if the average life today is greater than 70 years based on that sample. The sample would seem to indicate that it is so, but what is the probability that the mean of the sample does not reflect the true mean of the population? Use a level of significance of 0.05. POSSIBLE ANSWERS:  a) z = 1.02 rejects Ho b) z = 2.02 Ho is accepted c) z = 0.02 Ho is rejected d) z = 2.02 is rejected Ho

PROBLEM 5: Researchers from the Ministry of Industry and Commerce investigate the product content of a soft drink bottling company that announces that the bottles contain 32 ounces of liquid with a standard deviation of 2 ounces. For the above, they take a sample of 49 bottles and analyze the average liquid content in them and decide to reject the claim of the company if the average content is less than 31,671 ounces. Indicate which of the following options represents the value of alpha and beta, corresponding to the null hypothesis H0: μ = 32 that is tested against the alternative hypothesis H1: μ<32. To calculate suppose that later it was verified that the true average content of the bottles was of 31.5 ounces. POSSIBLE ANSWERS: a) alpha = 0.00124 beta = 0.00274 b) alpha = 0.0124 beta = 00.274 c) alpha = 0.1 beta = 0.2 d) alpha = 0.124 beta = 0.274

Answer 1

problem 1)

Ho :   µ =   5.50  
Ha :   µ <   5.50  
          
Level of Significance ,    α =    0.05  
sample std dev ,    s =    0.240  
Sample Size ,   n =    64  
Sample Mean,    x̅ =   5.23
          
degree of freedom=   DF=n-1=   63  
          
Standard Error , SE =   s/√n =   0.0300  
          
t-test statistic=   (x̅ - µ )/SE =    -9.00  
          
  
p-Value   =   0.0000   [excel function =NORMSDIST(z)]
Conclusion:     p-value<α, Reject null hypothesis   

so, answer is option d)  z = -9 is rejected Ho