Question

For each question, write out the null and alternate hypotheses numerically. Give the test statistic and p-value. Write out the equation of the test statistic but you do not have to evaluate it by hand. Then conclude with whether you reject or fail to reject the null hypothesis.

Chapter 9

1. (Question 98.) Toastmasters International cites a report by Gallop Poll that 40% of Americans fear public speaking. A student believes that less than 40% of students at her school fear public speaking. She randomly surveys 361 schoolmates and finds that 135 report they fear public speaking. Conduct a hypothesis test to determine if the percent at her school is less than 40%.

2. (Question 100.) According to an article in Bloomberg Businessweek, New York City's most recent adult smoking rate is 14%. Suppose that a survey is conducted to determine this year’s rate. Nine out of 70 randomly chosen N.Y. City residents reply that they smoke. Conduct a hypothesis test to determine if the rate is still 14% or if it has decreased.

Chapter 10

3. (Question 124). A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. The population standard deviations are two pounds and three pounds, respectively. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. Conduct a hypothesis test to determine if there is a difference in these two diets

4. (Question 13) Lesley E. Tan investigated the relationship between left-handedness vs. right-handedness and motor competence in preschool children. Random samples of 41 left-handed preschool children and 41 right-handed preschool children were given several tests of motor skills to determine if there is evidence of a difference between the children based on this experiment. The experiment produced the means and standard deviations shown Table 10.36. Conduct a hypothesis test to determine if there is a difference in motor competence

Left-handed Right-handed

Sample size                                        41                    41

Sample mean                                     97.5                 98.1

Sample St. Dev.                                 17.5                 19.2

Answer 1

98)

Ho :   p =    0.4                  
H1 :   p <   0.4       (Left tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   135                  
Sample Size,   n =    361                  
                          
Sample Proportion ,    p̂ = x/n =    0.3740                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0258                  
Z Test Statistic = ( p̂-p)/SE = (   0.3740   -   0.4   ) /   0.0258   =   -1.0099
                          
  
p-Value   =   0.1563   [excel function =NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis                       

100)

Ho :   p =    0.14                  
H1 :   p <   0.14       (Left tail test)          
                          
Level of Significance,   α =    0.05                  
Number of Items of Interest,   x =   9                  
Sample Size,   n =    70                  
                          
Sample Proportion ,    p̂ = x/n =    0.1286                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0415                  
Z Test Statistic = ( p̂-p)/SE = (   0.1286   -   0.14   ) /   0.0415   =   -0.2756
                          
  
p-Value   =   0.3914   [excel function =NORMSDIST(z)]              
Decision:   p value>α ,do not reject null hypothesis