Use the following to answer questions 7778 Of 250 adults who

Use the following to answer questions 77-78: Of 250 adults who tried a new multi-grain cereal, Wow!, 187 rated it excellent; of 100 children sampled, 66 rated it excellent.

77. Using the 0.1 significance level and the alternate hypothesis P1 not equal to P2, what is the null hypothesis?

A) P1 > P2

B) P1 < P2

C) P1 = P2

D) None of the above

78. What test statistic should we use?

A) z-statistic B) Right one-tailed test C) Left one-tailed test D) Two-tailed test E) None of the above

A study by a bank compared the average savings of customers who were depositors for three years or less, with those who had been depositors for more than three years. The results of a sample are:

<3yr >3yr

mean saving balance 1200 1250

standard devisation 100 250

sample size 100 150

79. What is the computed test statistic? ______________

80. For = 0.05, what is the critical value of z? __________

81. Assuming that the financial officer wants to show that there is a difference in the average savings balance between the two classes of depositors, what is the null hypothesis? _____________________

Use the following to answer questions 82-87: To compare the effect of weather on sales of soft drinks, a soda manufacturer sampled two regions of the country with the following results. Is there a difference in sales between the 2 regions?

reg A reg B

sample size 1000 1500

sales 400 500

82. What is the null hypothesis? _____________________

83. What is the alternate hypothesis? _______________________

84. What is the proportion of sales made in Market Area A? ______

85. What is the proportion of sales made in Market Area B? ______

86. Using the 1% level of significance, what is the critical value? _____

87. What is your decision? ____________________

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate Hypothesis, There Is Significance between them H1: p1 != p2
Test Statistic
Sample 1 : X1 =187, n1 =250, P1= X1/n1=0.748
Sample 2 : X2 =66, n2 =100, P2= X2/n2=0.66
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.723
Q^ Value For Proportion= 1-P^=0.277
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.748-0.66)/Sqrt((0.723*0.277(1/250+1/100))
Zo =1.662
| Zo | =1.662
Critical Value
The Value of |Z | at LOS 0.1% is 1.645
We got |Zo| =1.662 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Two Tailed ( double the one tail ) -Ha : ( P != 1.6617 ) = 0.0966
Hence Value of P0.1 > 0.0966,Here we Reject Ho

Q77.
C) P1 = P2

Q78.
Zo =1.662
Two Tailed