Question

In a study of
red/green color blindness, 950 men and 2550 women are randomly
selected and tested. Among the men, 85 have red/green color
blindness. Among the women, 7 have red/green color blindness. Test
the claim that men have a higher rate of red/green color
blindness.

(Note: Type ‘‘*p*_*m*′′‘‘p_m″ for the symbol
*p**m*pm , for example
** p_mnot=p_wp_mnot=p_w**
for the proportions are not equal,

(a) State the null hypothesis:

(b) State the alternative hypothesis:

(c) The test statistic is

(d) Is there sufficient evidence to support the claim that men
have a higher rate of red/green color blindness than women? Use a 5
% significance level.

**A.** Yes

**B.** No

(e) Construct the 95% confidence interval for the difference
between the color blindness rates of men and women.___
<(*p**m*−*p**w*)<___

Answer #1

The statistical software output for this problem is:

**Two sample proportion summary hypothesis
test:**

p_{1} : proportion of successes for population 1

p_{2} : proportion of successes for population 2

p_{1} - p_{2} : Difference in proportions

H_{0} : p_{1} - p_{2} = 0

H_{A} : p_{1} - p_{2} > 0

**Hypothesis test results:**

Difference | Count1 | Total1 | Count2 | Total2 | Sample Diff. | Std. Err. | Z-Stat | P-value |
---|---|---|---|---|---|---|---|---|

p_{1} -
p_{2} |
85 | 950 | 7 | 2550 | 0.086728586 | 0.006081039 | 14.262133 | <0.0001 |

**95% confidence interval results:**

Difference | Count1 | Total1 | Count2 | Total2 | Sample Diff. | Std. Err. | L. Limit | U. Limit |
---|---|---|---|---|---|---|---|---|

p_{1} -
p_{2} |
85 | 950 | 7 | 2550 | 0.086728586 | 0.0093182345 | 0.068465182 | 0.10499199 |

Hence,

a) Null: p_m = p_w

b) Alternative: p_m > p_w

c) Test statistic = 14.2621

d) Yes

e) 95% confidence interval:

0.0685 < (pm−pw) < 0.1050

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