Question

Recent research commissioned by Vodafone suggests that older workers are the happiest employees (BBC News, July 21, 2008). The report documents that 70% of older workers in England feel fulfilled, compared with just 50% of younger workers. A demographer believes that an identical pattern does not exist in Asia. A survey of 120 older workers in Asia finds that 75 feel fulfilled. A similar survey finds that 58% of 210 younger workers feel fulfilled.
At a 5% level of significance, test if older workers in Asia feel less fulfilled than their British counterparts.
a-1. Select the null and the alternative hypotheses.
H0: p ≥ 0.70; HA: p < 0.70
H0: p = 0.70; HA: p ≠ 0.70
H0: p ≤ 0.70; HA: p > 0.70
a-2. Calculate the sample proportion. (Round your answer to 3 decimal places.)
Sample proportion
a-3. Calculate the value of test statistic. (Negative value should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Test statistic
a-4. Calculate the p-value of the test statistic.(Round your intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)
p-value
a-5. What is the conclusion?
Older workers in Asia feel less fulfilled
Older workers in Asia do not feel less fulfilled
At a 5% level of significance, test if younger workers in Asia feel more fulfilled than their British counterparts.
b-1. Select the null and the alternative hypotheses.
H0: p = 0.50; HA: p ≠ 0.50
H0: p ≥ 0.50; HA: p < 0.50
H0: p ≤ 0.50; HA: p > 0.50
b-2. Calculate the sample proportion. (Round your answer to 2 decimal places.)
Sample proportion
b-3. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)
Test statistic
b-4. Calculate the p-value of the test statistic.(Round your intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)
p-value
b-5. What is the conclusion?
Younger workers in Asia feel more fulfilled
Younger workers in Asia do not feel more fulfilled

Answer 1

Answer:

H0: p ≥ 0.70; HA: p < 0.70

Sample proportion = 0.625

Test statistic = -1.79

Pvalue = 0.0367

Older workers in Asia feel less fulfilled

B.)

H0: p ≤ 0.50; HA: p > 0.50

0.58

2.35

0.0094

younger workers in Asia feel more fulfilled

Step-by-step explanation:

1.)

H0: p ≥ 0.70;

HA: p < 0.70

The test statistic :

(Phat - p) /sqrt(p(1-p)/n)

Phat = x / n = 75/120 = 0.625

1 - p = 1 - 0.7 = 0.3

(0.625-0.70) / sqrt(0.7*0.3/120)

-0.075 / 0.0418330

= - 1.79

Pvalue FROM Zscore calculator :

Pvalue = 0.0367

α = 5% = 0.05

Pvalue < α ; Reject then Null and conclude older workers in Asia feel less fulfilled than their British counterparts.

B.)

H0: p ≤ 0.50; HA: p > 0.50

Sample proportion, phat = 58% = 0.58

The test statistic :

(Phat - p) /sqrt(p(1-p)/n)

(0.58 - 0.50) / sqrt(0.58*0.42)/210)

0.08 / 0.0340587

Test statistic = 2.35

Pvalue FROM Zscore calculator :

Pvalue = 0.0094

α = 5% = 0.05

Pvalue < α ; Reject then Null and conclude younger workers in Asia feel more fulfilled than their British counterparts