Question

Marketers believe that 83.46% of adults in the U.S. own a cell phone. A cell phone manufacturer believes the proportion is different than 0.8346. 37 adults living in the U.S. are surveyed, of which, 23 report that they have a cell phone. Using a 0.01 level of significance test the claim.

The correct hypotheses would be:

• H0:p≤0.8346H0:p≤0.8346
  HA:p>0.8346HA:p>0.8346 (claim)
• H0:p≥0.8346H0:p≥0.8346
  HA:p<0.8346HA:p<0.8346 (claim)
• H0:p=0.8346H0:p=0.8346
  HA:p≠0.8346HA:p≠0.8346 (claim)

Since the level of significance is 0.01 the critical value is 2.576 and -2.576

The test statistic is: (round to 3 places)

The p-value is: (round to 3 places)

The decision can be made to:

• reject H0H0
• do not reject H0H0

The final conclusion is that:

• There is enough evidence to reject the claim that the proportion is different than 0.8346.
• There is not enough evidence to reject the claim that the proportion is different than 0.8346.
• There is enough evidence to support the claim that the proportion is different than 0.8346.
• There is not enough evidence to support the claim that the proportion is different than 0.8346.

Answer 1

Given:

P = 83.46% = 0.8346, n = 37, X = 23, = 0.01

Hypothesis:

F. Ho:p = 0.8346 HA: p ≠ 0.8346 (claim)   OR    A cell phone manufacturer believes the proportion is different than 0.8346

Calculation:

Critical value:

Z_/2 = Z _0.01/2 = 2.57

Test statistic:

P-value: 0.0005

P-value < , 0.0005 < 0.01, That is Reject Ho at 1% level of significance.

ANSWER: A Reject Ho

The final conclusion is that:

ANSWER: C

There is enough evidence to support the claim that the proportion is different than 0.8346.