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# Hypothesis Testing

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This presentation includes detailed information on Hypothesis testing for large and small samples, for two sample means. Briefed computational procedure with various case studies.

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### Hypothesis Testing

1. 1. HYPOTHESIS TESTING ONE TAIL & TWO TAIL TESTS
2. 2. HYPOTHESIS  Hypothesis: “Proposition or Supposition made from known facts as basis for reasoning or investigation” – The Oxford Dictionary.  Hypothesis Testing begins with an assumption, called a hypothesis, that we make about a population parameter.  Hypothesis Testing involves making two quantitative statements about some population parameter:  One based on a claim or belief or suspicion – Null Hypothesis  Other statement is opposite of the first – Alternative Hypothesis  Determining whether the null hypothesis is true or false is based on the sample information, but not by only intuition.  Null & Alternative Hypothesis covers all possible values of parameter. 2 BirinderSingh,AssistantProfessor,PCTE Ludhiana
3. 3. HYPOTHESIS  Null Hypothesis can be inferred from alternative hypothesis and vice a versa.  Fuel Consumption of Maruti Car is atleast 18 km/ltr  Null Hypothesis : FC ≥ 18 km/l or H0 : µ ≥ 18  Alternative Hypothesis : FC < 18 km/l or H1 : µ < 18  ‘18’ is called hypothesized value and is denoted by µH0  Plant fills exactly 500 ml of milk in every bottle  H0 : µ = 500  H1 : µ < 500, µ > 500, µ ≠ 500,  µH0 = 500  My Secretary does not make more than 5 errors in a letter  H0 : µ ≤ 5  H1 : µ > 5  µH0 = 5 3 BirinderSingh,AssistantProfessor,PCTE Ludhiana
4. 4. LEVEL OF SIGNIFICANCE  LOS is denoted by α = 1 – CL  Probability levels are used to decide whether to accept or reject null hypothesis  LOS is probability of rejecting a true null hypothesis  LOS = 5% means that experimenter runs the risk of rejecting a correct hypothesis of 5 out of 100 times. 4 BirinderSingh,AssistantProfessor,PCTE Ludhiana
5. 5. REGION OF ACCEPTANCE OR REJECTION  LOS is mainly employed in decision making problems because it distinguishes between true regions known as region of acceptance or rejection.  A sample of values such that if sample statistic falls in range, the null hypothesis is accepted & is called Range of Acceptance and where rejected is called Range of Rejection. 5 BirinderSingh,AssistantProfessor,PCTE Ludhiana
6. 6. COMPUTATIONAL PROCEDURE IN HYPOTHESIS TESTING  Define Null & Alternative Hypothesis  Select estimator & determine its distribution  Select Significance Level  Define decision rule (One Tail or Two Tail Test)  Compute Critical Value/s  In case of Two Tail Test  CVL =µH0 − 𝒛α/ 𝟐 𝝈 𝒙  CVR =µH0 + 𝒛α/ 𝟐 𝝈 𝒙  In case of One Tail Test  CV =µH0 − 𝒛 𝝈 𝒙 (Left Tail Test)  CV =µH0 + 𝒛 𝝈 𝒙 (Right Tail Test)  Make the Statistical Decision by checking whether the sample mean lies in region of acceptance or rejection  Make the managerial decision 6 BirinderSingh,AssistantProfessor,PCTE Ludhiana
7. 7. HYPOTHESIS TESTING OF MEANS PRACTICE PROBLEMS – TWO TAIL  A bottling machine is supposed to fill 500 ml of milk in a bottle. However, the contents are not always exact. The quantity is known to be normally distributed with a standard deviation of 10 ml. A sample check of 36 bottles revealed mean of 515 ml. The manager of bottling plant wants to know if machine is working satisfactorily? Test at 5% LOS. (496.73≤ µ≤ 503.27) (Rejection Region) (Machine not OK) 7 BirinderSingh,AssistantProfessor,PCTE Ludhiana
8. 8. HYPOTHESIS TESTING OF MEANS PRACTICE PROBLEMS – ONE TAIL  A manufacturer claims that the mean life of a tube is 4000 hrs. (at least). A retailer wants to find out if manufacturer claim is correct or not. Random sample of 65 tubes checked by him revealed a mean life of 3982 hrs with a standard deviation of 80 hrs. Should the tubes be accepted at 5% level of confidence? (CV = 3983.67) (Rejection Region) (Retailer rejects) 8 BirinderSingh,AssistantProfessor,PCTE Ludhiana
9. 9. HYPOTHESIS TESTING OF MEANS PRACTICE PROBLEMS – ONE TAIL  There are 1000 customers who are authorized credit purchase from a grocery store. The store has targeted that, on an average, credit sales in a month should not exceed Rs. 10000. It is known from past experience that SD of credit sales is Rs. 500. A random sample of 81 such customers revealed a mean of Rs. 10250 towards credit sales. Would you conclude at 5% significance level that store is achieving its targets? (CV = 10087.65) (Rejection Region) (Not achieving) 9 BirinderSingh,AssistantProfessor,PCTE Ludhiana
10. 10. HYPOTHESIS TESTING OF MEANS PRACTICE PROBLEMS – TWO TAIL  A TV documentary telecast on ‘Nikat Darshan’ channel claimed that adult Punjabi males are 10 kg over weight on an average. 18 randomly selected individuals showed an excess weight of 11.6 kg with SD of 2.7 kg. Check at LOS of 0.01, is there any reason to doubt validity of claim. Assume normal distribution of excess weight. (8.16≤ µ≤ 11.84) (Acceptance Region) (Claim is correct)  Here t α but not tα/2 as area mentioned is under both tails 10 BirinderSingh,AssistantProfessor,PCTE Ludhiana
11. 11. HYPOTHESIS TESTING OF MEANS PRACTICE PROBLEMS – ONE TAIL  A manufacturer has claimed that life of a refrigerator produced by his company is atleast 14500 hrs. From a sample of 25 refrigerators, sample mean was found to be 13600 hrs with SD of 2100 hrs. Would you accept the manufacturer’s claim at 0.01 LOS? (CVL = 13453.36) (Acceptance Region) (Claim is correct)  Here t 2α but not tα as area mentioned is under one tail 11 BirinderSingh,AssistantProfessor,PCTE Ludhiana
12. 12. HYPOTHESIS TESTING OF PROPORTIONS PRACTICE PROBLEMS – ONE TAIL  A B-School has advertised that at least 80% of the students are placed in good jobs during interviews. In a sample survey of 100 ex-students, it emerged that 74 were placed in good jobs during recruitment. Validate claim of B School at 0.05 LOS. (CVL = 0.734) (Acceptance Region) (Claim is correct) 12 BirinderSingh,AssistantProfessor,PCTE Ludhiana
13. 13. HYPOTHESIS TESTING OF PROPORTIONS PRACTICE PROBLEMS – TWO TAIL  HR Sol. Pvt. Ltd. feels that in NCR region, 15% of MBA students opts for HR. In a sample survey of 120 students, it was found that 22 of them had opted for HR in 2nd year. At 0.02 LOS, is there any evidence to suggest that firm’s perception is correct? (0.074≤ pH0 ≤ 0.226) (Acceptance Region) (Perception is correct) 13 BirinderSingh,AssistantProfessor,PCTE Ludhiana
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15. 15. DECISION FLOW DIAGRAM - ESTIMATION 15 BirinderSingh,AssistantProfessor,PCTE Ludhiana Start Is n≥30 Is pop. Known to be normally distributed Use ‘Z’ table Stop Use a Statistician Is SD known ? Use ‘Z’ table Stop Use ‘t’ table Stop