Question

In order to conduct a hypothesis test for the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting sample mean and sample standard deviation are calculated as 4.8 and 0.8, respectively. (You may find it useful to reference the appropriate table: z table or t table) HOT #3 4.5 against Ha: > 4.5 a-1. Calculate the value of the test statistic. (Round all intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.) Test statistic a-2. Find the p-value O p-value s 0.01 0.01<p-value s 0.025 O 0.025 <p-value s 0.05 O 0.05< p-values 0.10

Answer 1

Given that the sample size,n= 24 (small sample) Mean of the sample 1 = 4.8 The sample standard deviation ,S=0.8 Null hypothesis: 40:4<4.5 Alternative Hypothesis: H: 4 > 4.5 Level of significance, a = 5% = 0.05 Degrees of freedon = n-1= 24 -1 = 23 Population mean 4= 4.5, 1-4 4.8-4.5 a. 1) The test statistic t = = 1.8371 S/ 0.8/ va 24 Test statistic t = 1.837 a.2)p-Value: P(Z > 1.837) = 1-F(1.84) = 1-0.9671=0.0396 Hence Option (3) 0.025 <p-Value <0.05 is correct a. 3) Since p-value = 0.0396 <0.05 we Reject H, Option (1) Reject H, since p-value is not greater than a a.4) Option (1) We conclude that the population mean is greater than 4.5 *** For b. 1,5-2,5.3, problem is not uploded.