According to Thomson Financial, through January 25, 2006, t for the 4th quarter

Question

According to Thomson Financial, through January 25, 2006, t for the 4th quarter of 2012, 212 of a random sample of 275 companies reported profits that had beaten estimates. Use this latest information to 20answer the following questions. (See exercise 38 on page 369 of your textbook for a similar problem.) 21 Question 1A . Does the data show the root on o companies in he 4th quarter of 2012 hr beat estima es is grea e than 73% aa- 5, 25 25 Step 1 27 28 25 30 Srep2 Srep3 il ow 34i the hypothesis is one tailed 32 35 36 07 38 Fill in row 38 the hypothesis is twotailed The smaller number must be typed first 40 Step 4 42 43 Step6 45 46 Step 7:Fillinow 48 the Ztable is appropriate P-value Filln row 52 t thet abs spropae The lower boundany must go onthe left and d the upper boundary on the right P-value Quenon E. Construct a 99% condenc e interval for the true proportion of comparies in the 4th quarter of 2012 that beat estimates Lower Endpoin Upper Endpoinj

Explanation / Answer

1A.

Step 1:

H0: p = 0.73

Ha: p > 0.73

Step 2:

Observed proportion = 212 / 275 = 0.7709091

Step 3:

For significance level of 0.05, and one-sided tail test, z = 1.64

Standard error of sample proportion = sqrt(0.73*(1-0.73)/275) = 0.02677176

Critical value of p at significance level of 0.05 = 0.73 + 1.64 * 0.02677176 = 0.7739057

Fill in row 34 - Reject H0 if observed p > 0.7739057

Step 4:

Observed p < Critical value of p

Step 5:

Accept H0

Step 6:

Z = (0.7709091 - 0.73)/0.02677176 = 1.528069

Step 7:

Fill in Row 48: P-value = P(Z > 1.528069) = 0.0632477

1B.

Z-value for 99% confidence interval is 2.58

99% confidence interval is,

(0.7709091 - 2.58 * 0.02677176, 0.7709091 + 2.58 * 0.02677176)

(0.701838, 0.8399802)

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