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A test statistic is used in a hypothesis testing when you are deciding to support or reject the null hypothesis. In large sample test concerning the population mean. the test statistic to be used is the at. The ztest statistic is used when the sample size is greater than 30 {n 230]. or when the population is normally distributed and a is known. Formula: where: z: = z - test statistic or z - computed .L = sample mean no = population mean o = population standard deviation :1 = sample size Steps in hypothesis testing using the z-tsat statistic 1. State the hypotheses 2. Identify the level of significance and determine if the test is two-tailed or one-tailed. 3. Compute the test statistic 4. Determine the critical value. draw the normal curve. and identify the critical region 5. State vour decision and make a final conclusion Example 1. A light bulb manufacturer claims that the average lifetime of a bulb is 30 months. The standard deviation is 3" months. Forty bulbs are selected and the average lifetime is found to be 26 months. Should the manufacturer's statement he rejected at a = 0.05? GSC-CiDLRMSESSLM, VJ. 2.00. Effective ApJ'I'fZ'f, 2021 Solution: Step 1. Ho: p = 30 months Step 4. Since or = 0.05 and it is him-tailed, Ha: pr at 30 months the critical values are 2,1,2 = $1.960 Step 2. a: = 0.05; $ = 0.025; twcrtailed test Step 3. Test statistic Given: x=26.p=30.o=7,n=40 z: = 1-11: \":30 = j = #4" = 3.r.1 3.61 4.960 1.960 47- 741 m ' Step 5. DecisionJ'Conclusion: Since Zc =-3.61 4-3 the critical value is 2,, = 1.282 Step 2. a: = 0.10; one-tailed test Step 3. Test statistic Given: I:50.5,p=48,o=3.8,n=35 1.232 3.91 1,. 50543 25 25 z=a=n=-n-==3.91 a: a; m: \"L\" Step 5. DecisionJ'Conclusion: Since Zc =3.91 > Z a =1.282, thus, we reject the Ho. Therefore, there is enough evidence to support the claim that a can of juice contains a mean carbo content of over 43g. m Let Us Apply Activity 3: "LET'S FIND IT!" A researcher claims that the average load consumption of Grade 11 students for their online class is $3,000 per month. In a sample of 36 students, the average monthly load consumption was #2,750 with the standard deviation of P550. Is there enough evidence to support the claim at a = 0.05