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Assignment 3 week 9-week 11


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                                STATISTICS (STAT-101)



                                                                                                                                     Marks- 30


Answer all the Questions on the same question paper.




State whether the following statements are True or False. (6 marks, 1 Mark Each)


  1. A type I error is the mistake of rejecting the null hypothesis when it is actually false.
  2. Two samples are independent if the sample values selected from one population are not related to the sample values from the other population. 
  3. The null hypothesis (denoted byH0) is  a statement that the value of a population parameter is equal to some value.
  4. In case of hypothesis testing for a sample, the t statistic is used if  is not known and sample size n is greater than 5
  5. A claim that two population proportions are equal, each of the two samples must satisfy the requirement that and .
  6. In an unpaired samples t-test with sample sizes n1= 21 and n2= 11, the value of t should be obtained at 32 degree of freedom.





 (Multiple Choice Questions)                              (6 marks, 1 Mark Each)

  1. If p-value <  α, then
    1. Reject H0
    2. Accept H0
    3. Reject H1
    4. All the above


  1. The MEAN of the Student t_distributionis
    1.  equal to 0
    2.  less than 1
    3.  less than 0
    4.  greater than 1


  1. A decision in a hypothesis test can be made by using a :
    1. P-value
    2. Critical Value
    3. A and B
    4. None of the above


  1. When carrying out a large sample test of H0:  = 10 vs. H: > 10 by using a rejection point, we reject H0 at level of significance   when the calculated test statistic is:
    1. Less than
    2. Less than -
    3. Greater than
    4. Greater than


  1. A randomly selected sample of 500 college students was asked whether they had ever used the drug Ecstasy. Sixteen percent (16% or 0.16) of the 500 students surveyed said they had. Which one of the following statements about the number 0.16 is correct?
  1. It is a population proportion.
  2. It is a margin of error.
  3. It is a sample proportion.
  4. It is a randomly chosen number.


  1. Sample sizes n1 = 100, n2 = 100 and numbers x1 = 39, x2 = 41 of successes to find the pooled estimate
    1. 0.4
    2. 0.8
    3. 0.36
    4. 0.48



Part-II (Multiple Choice Questions)                     (6 marks, 1 Mark Each)























Section –III

Answer the following Essay Type Questions                 (18 marks, 3 Mark Each)


  1. Suppose the national unemployment rate is 3%.  In a survey of n = 450 people in a rural Wisconsin county, 22 people are found to be unemployed.  County officials apply for state aid based on the claim that the local unemployment rate is higher than the national average.  Test this claim at the .05 significance level.



  1. Suppose we would like to determine if the typical amount spent per customer for dinner at a new restaurant in town is more than $20.00.  A sample of 49 customers over a three-week period was randomly selected and the average amount spent was $22.60.  Assume that the standard deviation sis known to be $7.50.  Using a 0.05 level of significance, would we conclude the typical amount spent per customer is more than $20.00?



  1. The scores on an aptitude test required for entry into a certain job position have a mean at most 500. If a random sample of 36 applicants have a mean of 546 and a standard deviation of 120, is there evidence that their mean score is different from the mean that is expected from all applicants?. Use a 0.05 level of significance.



  1. The table show the number satisfied in their work in a sample of working adults with a college education and in a sample of working adults without a college education. Do the data provide sufficient evidence that a greater proportion of those with a college education are satisfied in their work? Use a significance level of α = 0.05 to test the claim that p1 < p2.




College Education

No College Education

Number satisfied in their work


Number in sample










Q. 5 & 6.Use the following information to answer Questions5 and 6:


Given the following data of two independent samples of normally distributed populations




Population 1

Population 2





  1. Test the claim that  at the α=0.05 level of significance
  2. Construct a 95% confidence interval about  .




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