Use a t-test to test the claim about the population mean at the given level of s
ID: 3325031 • Letter: U
Question
Use a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed Claim: = 52,900; -0.01 Sample statistics: x-54,044, s-2700, n-17 Click the icon to view the t-distribution table What are the null and altemative hypotheses? Choose the correct answer below A. Ho: 52,900 Ha: 52,900 OB. Ho: =52.900 Hai 52,900 OD. Ho: #52,900 Ha: = 52,900 What is the value of the standardized test statistic? The standardized test statistic is(Round to two decimal places as needed.) What is(are) the critical value(s)? The critical value(s) is(are) (Round to three decimal places as needed. Use a comma to separate answers as needed.) Decide whether to reject or fail to reject the null hypothesis 0 A. Fail to reject Ho. There is not enough evidence to reject the claim 0 B. Fail to reject Ho. There is enough evidence to reject the claim ° C. Reject Ho . There is enough evidence to reject the claim. 0 D. Reject Ho . There is not enough evidence to reject the claim.Explanation / Answer
Solution:
Correct answer for null and alternative hypothesis is given as below:
H0: µ = 52,900
Ha: µ 52,900
Correct answer is B.
Standardized test statistic is given as below:
Standardized test statistic = t = (Xbar - µ) / [S/sqrt(n)
We are given
Xbar = 54044,
S = 2700
n = 17
df = n – 1 = 16
= 0.01
Standardized test statistic = (54044 – 52900) / [2700/sqrt(17)]
Standardized test statistic = 1.75
Critical value = -2.921, 2.921
(By using t-table)
Decision:
Here, test statistic value is lies between given two critical values, so we fail to reject the null hypothesis H0. So, correct answer is A.
A. Fail to reject H0. There is not enough evidence to reject the claim.
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