null and alternative hypothesis.pptx
- 1. Formulating Appropriate Null and Alternative Hypotheses on a Population Mean
- 2. Hypothesis testing is the process of using statistical tests to determine whether an observed difference between two or more samples is statistically significant or not A statistical hypothesis is a statement about a parameter and deals with evaluating the value of parameter.
- 3. There are always two hypotheses: the null and alternative hypotheses.
- 4. Note: 𝐻𝑜 always has = symbol in it. 𝐻𝑎 never has an = symbol in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = (equal sign) in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. Notice also that the notation of alternative hypothesis complements the null hypothesis.
- 5. 1. The average height of all Grade 11 students in Senior High School is 169cm. Is this claim true 𝑯𝒐: The average height of all Grade 11 students is 169 cm. / 𝑯𝑶:𝝁 = 𝟏𝟔𝟗 𝑯𝒂: The average height of all Grade 11 students is not 169 cm./ 𝑯𝒂: 𝝁 ≠ 𝟏𝟔𝟗
- 6. 2. The average price per square meter of residential lot in an exclusive subdivision is above ₱15,000. A buyer wants to test the agent’s claim. 𝑯𝒐: 𝝁 = ₱𝟏𝟓, 𝟎𝟎𝟎 or 𝑯𝒐: 𝝁 ≤ ₱𝟏𝟓, 𝟎𝟎𝟎 𝑯𝒂: 𝝁 > ₱𝟏𝟓, 𝟎𝟎𝟎 (claim)
- 7. 3. Holistic Fitness Center claims that their members reduced an average of 13 pounds after joining the center. An independent agency wanted to check this claim took sample of 40 members and found that they reduced an average of 12 pounds with the standard deviation of 4 pounds. Determine the null and alternative hypothesis. Solution: In this example, the parameter to be tested is the average and the claim is reduced of 13 pounds. The claim that pertains to the parameter has the notation of < 𝟏𝟑. The null hypothesis would 𝑯𝒐: 𝝁 = 𝟏𝟑 or be 𝑯𝒐: 𝝁 ≥ 𝟏𝟑 𝑯𝒐 : 𝝁 ≥ 𝟏𝟑 or 𝑯𝒐 : 𝝁 = 𝟏𝟑 𝑯𝒂: 𝝁 < 𝟏𝟑 (claim)
- 8. 4. The treasurer of a municipality claims that the average net worth of families in the municipality is at least ₱730,000. A random sample of 50 families from this area produced a mean net worth of ₱860,000 with standard deviation of ₱65,000. What are the null and alternative hypotheses? 𝑯𝑶: µ = ₱𝟕𝟑𝟎, 𝟎𝟎𝟎 (claim) or 𝑯𝑶: µ ≥ ₱𝟕𝟑𝟎, 𝟎𝟎𝟎 𝑯𝒂: µ < ₱𝟕𝟑𝟎, 𝟎𝟎𝟎
- 9. 5. An academic organization claimed that Grade 11 students’ study time is at most 240 minutes per day, on average. Another survey was conducted to find whether the claim is true. The group took a random sample of 30 students and found a mean study time of 300 minutes with standard deviation of 90 minutes. What are the null and alternative hypotheses? 𝑯𝑶: µ ≤ 𝟐𝟒𝟎 or 𝑯𝑶: µ = 𝟐𝟒𝟎 (claim) 𝑯𝒂: µ > 𝟐𝟒𝟎
- 10. One-Tailed and Two-Tailed Test The table below shows the null and alternative hypotheses stated together with the directional test.
- 11. Determine the hypotheses and the hypothesis test. 1. Teacher A wants to know if mathematical games affect the performance of the students in learning Mathematics. A class of 45 students was used in the study. The mean score was 90 and the standard deviation was 3. A previous study revealed that 𝝁 = 𝟖𝟓 and the standard deviation 𝝈 = 𝟓. 2. A piggery owner believes that using organic feeds on his pigs will yield greater income. His average income from the previous year was ₱120, 000. State the hypothesis and identify the directional test. 3. The average waiting time of all costumers in a restaurant before being served is less than 20 minutes. Determine the hypotheses and the directional test.