According to Thomson Financial, through January 25, 2006, the majority of compan

Question

According to Thomson Financial, through January 25, 2006, the majority of companies reporting profits had beaten estimates. Now suppose that for the 4th quarter of 2012, 196 of a random sample of 265 companies reported profits that had beaten estimates. Use this latest information to answer the following questions

1. Does the data indicate the proportion of companies in the 4th quarter of 2012 that beat estimates is greater than 67% at a=0.05?

Step 1 : find Ho _____ (u, p) _____( <, >,=, less than or equal to, greater than or qual to, not greater or less than) _____( answer must be typed to 4 decimal places)

find Ha: _____(u,p) _____(<, >, = , less than or equal to, greater than or equal to, not greater or less than) _____ (answer must be typed to 4 decimal places)

Step 2: ____ ( Z crit, t crit, z stat, t stat) = ____ (+, -, plus minus) _____ (Answer must be typed to either 2 or 3 decimals depending on whether the z or t table is appropriate)

Step 3: Fill in below if the hypothesis one tailed

Reject H0 if ____( Z crit, t crit, z stat, t stat) _____( <,>,=, less than or equal to, greater or less than, not greater or less than) _____ ( answer must be typed to either 2 or 3 decimals depending on whether the z or t table is appropriate) . or _____ _______ ______( answer must be typed to either 2 or 3 decimals depending on whether the z or t table is approprite)

Fill in below if the hypothesis is wo tailed. the smaller number must be typed first

Reject H0: if ____( z crit, t crit, z sta ,t stat) ______(<,>,=, less than or equal to, greater than or equal, not greater or less than) _____( answer must be typed either 2 or 3 decimals depending on whether the z or table is appropriate).

Step 4: _____ ( z crit , t crit, z stat, t stat) = _____( answer must be typed either 2 or 3 decimals depending on whether the z or t table is appropriate)

Step 5 : _____ ( reject or fail to reject) H0

Step 6: ____ ( TISETC, TINSETC) _____(u,p) _______(<,>, <=, >=, not greater than or less than) ______ ( answer must be typed to four decimals)  

step 7 : fill in below if the z table is appropriate

P-value = _____( answer must be typed to four decimals)

Fill in below if the t table is appropriate. The lower boundary must go on the left and the upper boundary on the right

____(answer must be typed to 4 decimals) ____ (<,>, <=,>=, not greater than or less than) p-value ____(<,>, <=,>=, not greater than than or less than)

construct a 99% confidence interval for the true proportion of companies in the 4th quarter of 2012 that beat estimates.

Lower Endpoint ______ ( answer must be typed to four decimals) Upper Endpoint_____( answer must be typed to four decimals)

Explanation / Answer

1)
H0 : p = 0.67
Ha : p >= 0.67

2)
z critical value
z > = 1.645

3)
Reject H0 if z >= 1.645

4)
Test statistic:
P= 0.77,n = 256

z = ( P - p) /sqrt( p * ( 1 -p) /n)
= ( 0.77 -0.67) / sqrt( 0.67 * 0.33/256)
= 3.403

5)
Reject H0 because z >= 1.645

6)
P value is calcualted using z = 3.403
P value = 0.000333.

7)
z value at 99% = 2.576
CI = p +/- z * sqrt(p * (1 -p) / n)
= 0.67 +/- 2.576 * sqrt( 0.67 * 0.33/256)
= (0.5943 , 0.7457)

Lower Endpoint 0.5943
Upper Endpoint 0.7457

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