Question

1. Marketers believe that 62.79% of adults in the U.S. own a cell phone. A cell phone manufacturer believes the proportion is different than 0.6279. 32 adults living in the U.S. are surveyed, of which, 18 report that they have a cell phone. Using a 0.01 level of significance test the claim. The correct hypotheses would be:

H 0 : p ≤ 0.6279 H 0 : p ≤ 0.6279 H A : p > 0.6279 H A : p > 0.6279 (claim) H 0 : p ≥ 0.6279 H 0 : p ≥ 0.6279 H A : p < 0.6279 H A : p < 0.6279 (claim) H 0 : p = 0.6279 H 0 : p = 0.6279 H A : p ≠ 0.6279 H A : p ≠ 0.6279 (claim) Correct

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)

2. A dietician read in a survey that 61.7% of adults in the U.S. do not eat breakfast at least 3 days a week. She believes that the proportion that skip breakfast 3 days a week is different than 0.617. To verify her claim, she selects a random sample of 60 adults and asks them how many days a week they skip breakfast. 38 of them report that they skip breakfast at least 3 days a week. Test her claim at αα = 0.05.

The correct hypotheses would be:

• H0:p≤0.617H0:p≤0.617
  HA:p>0.617HA:p>0.617 (claim)
• H0:p≥0.617H0:p≥0.617
  HA:p<0.617HA:p<0.617 (claim)
• H0:p=0.617H0:p=0.617
  HA:p≠0.617HA:p≠0.617 (claim)

Since the level of significance is 0.05 the critical value is 1.96 and -1.96
The test statistic is: (round to 3 places)
The p-value is: (round to 3 places)

3. Marketers believe that 62.79% of adults in the U.S. own a cell phone. A cell phone manufacturer believes the proportion is different than 0.6279. 32 adults living in the U.S. are surveyed, of which, 18 report that they have a cell phone. Using a 0.01 level of significance test the claim.

The correct hypotheses would be:

• H0:p≤0.6279H0:p≤0.6279
  HA:p>0.6279HA:p>0.6279 (claim)
• H0:p≥0.6279H0:p≥0.6279
  HA:p<0.6279HA:p<0.6279 (claim)
• H0:p=0.6279H0:p=0.6279
  HA:p≠0.6279HA:p≠0.6279 (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)

Answer 1

1) H₀: P = 0.6279

   H₁: P 0.6279

= 18/32 = 0.5625

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                            = (0.5625 - 0.6279)/sqrt(0.6279 * (1 - 0.6279)/32)

                            = -0.765

P-value = 2 * P(Z < -0.765)

           = 2 * 0.222 = 0.444

2) H₀: P = 0.617

H₁: P 0.617

= 38/60 = 0.633

The test statistic z = ( - P)/sqrt(P(1 - P)/n)

                            = (0.633 - 0.617)/sqrt(0.617 * (1 - 0.617)/60)

                            = 0.255

P-value = 2 * P(Z > 0.255)

           = 2 * (1 - P(Z < 0.255))

          = 2 * (1 - 0.601)

          = 0.798