Question

Nexium is a drug that can be used to reduce the acid produced by the body and heal damage to the esophagus due to acid reflux. The manufacturer of Nexium claims that more than 94% of patients taking Nexium are healed within 8 weeks. In clinical trials, 213 of 224 patients suffering from acid reflux disease were healed after 8 weeks.

Report your answers to three decimal places, where applicable.

np₀(1-p₀) = ______, which is  (less / greater) than 10.

The necessary condition for the normal approximation test of proportions  (is / is not) satisfied for this sample. Therefore, our conclusion in Homework 1-1 regarding the manufacturer's claim  (is / is not) valid.

Answer 1

Solution:

Given:

Claim: more than 94% of patients taking Nexium are healed within 8 weeks.

Thus p₀ = 0.94

Sample size = n = 224

x = Number of  patients suffering from acid reflux disease were healed after 8 weeks.= 213

Part a)

n*p₀ * (1-p₀)= 224 * 0.94 * (1-0.94) = 224 * 0.94 * 0.06 = 12.63336 = 12.634

Thus n*p₀ * (1-p₀)= 12.634 which is greater than 10.

The necessary condition for the normal approximation test of proportions is satisfied for this sample.

Therefore, our conclusion in Homework 1-1 regarding the manufacturer's claim is valid.

Steps for hypothesis testing:

Step 1) State H0 and H1:

H0: p =0.94 Vs H1: p >0.94

Step 2) Find z test statistic value:

P Po Pox(1-po n

213 0.9509 224

Thus

0.9509 0.94 0.94x (1-0.94) 224

0.0109 2 0.94x0.06 224

0.0109 V0.0002518

0.0109 0.0158678

0.69

Step 3) Find p-value:

p-value = P( Z > z test statistic value)

p-value = P( Z > 0.69)

p-value =1 - P( Z < 0.69)

Look in z table for z = 0.6 and 0.09 and find area.

.00 .01 .02 .03 .04 .05 .06 .07 .08 09 .5279 .$359 .5040 .5080 5160 .5239 .5319 0.0 .5000 .5120 5199 6753 6141 6517 5879 7224 .5517 .5714 0.1 .5398 .5438 5478 .5557 .5596 .5636 .5675 .5871 5910 .5948 5987 .6026 .6064 .6103 0.2 .5793 .5832 .6331 .6368 .6443 .6480 0.3 .6179 .6217 .6255 .6293 6406 0.4 .6554 6591 6628 .6664 .6700 6736 .6772 .6808 6844 .6915 7019 7054 7088 7123 7157 7190 0.5 6950 .6985 7517 7549 0.6 57 2201 כ 7257 7389 7422 7454 7486

P( Z< 0.69 ) = 0.7549

Thus

p-value =1 - P( Z < 0.69)

p-value =1 - 0.7549

p-value = 0.2451

Step 4) Decision rule:

Reject H0, if p-value < 0.05 level of significance, otherwise we fail to reject H0.

Since p-value= 0.2451 > 0.05 level of significance,we fail to reject H0.

Step 5) Conclusion:

There is not sufficient evidence to support the manufacturer of Nexium claim that more than 94% of patients taking Nexium are healed within 8 weeks.