Study the given examples below. Example 1: According to a study conducted by the Grade 12 students, P155 is the average monthly expense for cell phone loads of senior high school students in their province. A Statistics student claims that this amount has increased since January of this year. Do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of P165 for cell phone loads? Using 5% level of significance, assume that a population standard deviation is P52. Solution: Given: 155 0 - 52 = 0.05 1 = 165 1 = 50 Step 1: State the Null Hypothesis: null and alternative The average monthly expense for cellphone loads is hypotheses. P155. Hot / = 155 Alternative Hypothesis: The average monthly expense for cellphone loads is more than P155. Ha: H > 155 Step 2: Determine Since the population mean is being tested, the the test statistic, population standard deviation o is known, and n > then compute its test | 30, the appropriate test statistic is the z-test. value. X-H 165-155 10 7= 52 7.35 V50 2 = 1.361 (test statistic or z - computed value) Step 3: Find the critical value using Table 1: 2 - Critical Value the z-Critical Value Type of Test Table One tailed Level of Test Two-tailed Test Significance a -.05 or 5% 2 - $1.645 & $1.960 Since a -0.05 and the alternative hypothesis H:u > 155 is directional (right-tailed test), the critical value is z = 1.645.Practice More Very good! You made it this far. Let us continue rolling! Perform hypothesis testing for the following problems. 1. Tagum City Division determined students' Body Mass Index (BMI) at the opening of classes. It has been recorded that the average height of SHS female students is 154.2 centimeters with a standard deviation of 9 centimeters. One school claim that their female SHS students has an average height more than 154.2 cm. The school nurse conducted her own study and she randomly selected 40 female students. In her study, she got an average of 156.7 centimeters. Is there a reason to believe the claims of the school? Use 5% level of significance in testing the hypothesis. 2. A researcher reports that the average IQ level of SHS students enrolled in STEM Academic track is 110. A sample of 20 students has a mean IQ level of 106 with a standard deviation of 9. At 5% level of significance, test the claim that the IQ level of SHS students under the STEM Academic track is 110. 3. A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 750 hours. A random sample of 36 light bulbs has a mean life of 745 hours with a standard deviation of 60 hours. Do you have enough evidence to reject the manufacturer's claim? Use a= 0.05Step 4: Draw the curve, show the Non-Rejection rejection and non- Region Rejection Region rejection regions, then make decision. 25 2 15 1 05 0 03 25 1.361 1.645 *Recall that the From Table 1, critical region corresponds to the Right-tailed test statistic > (critical value) |Reject H, and support H rejection of the null test (test statistic)