Q1 A sample is used to obtain a 95 confidence interval for t

Q1) A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 10.89 to 13.21. If the same sample had been used to test H0: = 12 vs. H1: 12, H0 could not be rejected at the 0.05 level.
a. True  
b. False

Q2) In order to determine the p-value, which of the following is not needed?
   a. Whether the test is one-tail or two-tail.   
   b. The value of the test statistic.   
   c. The level of significance.   
   d. All of these choices are true.   

Q3) In testing the hypotheses H0: = 50 vs. H1: 50, the following information is known: n = 64, = 53.5, and = 10. The standardized test statistic z equals:
   a. 2.80   
   b. -1.96   
   c. 1.96   
   d. -2.80   

Q4) In testing the hypotheses H0: = 75 vs. H1: < 75, if the value of the test statistic z equals -2.42, then the p-value is:
   a. 0.0078   
   b. 2.4200   
   c. 0.9922   
   d. 0.5078   

Q5) For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is:
   a. smaller than -1.96 or greater than 1.96   
   b. smaller than 1.96 or greater than -1.96   
   c. greater than 1.645 or less than -1.645   
   d. greater than -1.96 or smaller than 1.96   

Solution

Ans 1 ) FALSE

Using empirical formula for 95 % confirence interval

U+2sd=13.21

U-2sd=10.89

2u=24.1

U = 12.05 this is xbar for z score

Using u we can find sd

Z SCORE = 12.05-12/0.58

= 0.0862

using this we can find probability which is 0.0862

comparing this to 0.05 we have 0.0862>0.05

we can reject ho