A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 279 vinyl gloves, 60% leaked viruses. Among 279 latex gloves, 14% leaked viruses. See the accompanying display of the technology results. Using a 0.10 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves. Let vinyl gloves be population 1. Identify: null, alternative hypothesis, test statistic, and P-value.

The P-value is (1) the significance level ?, so (2) the null hypothesis. There is (3) evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

1) greater than / less than 2) reject / fail to reject 3) sufficient / insufficient

(Table at bottom of question)

Technology results:

Pooled proportion: 0.37

Test statistic, z: 11.3049

Critical z: 1.2816

P-value: 0.0000

80% Confidence interval: 0.4163430 < p1 ? p2 < 0.5083882

a) H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

The P-value is less than the significance level.

Therefore, Reject the null hypothesis

In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

Step-by-step explanation:

(a) From the information given, we can identify the null hypothesis and alternative hypothesis.

H0: Null Hypothesis: P1 = P2

HA: Alternative Hypothesis:P1> P2

(b) n1 which is size of sample 1 = 279

p1 which is proportion of sample 1= 0.60

n2 which is size ofsample 2 = 279

p2 which is proportion of sample 2 = 0.14

P=n1p1+n2p2 / n1+n2

=279 × 0.60+279 × 0.14/279+279

=0.37

Q = 1- P = 0.63

SE= √PQ(1/n1+1/n2)

= √ 0.37 × 0.63(1/279+1/279)=0.0409

So,

Test statistic is:

Z = (p1 - p2) /SE

= (0.60 - 0.14)/0.0409

= 11.3049

(c) The able of Area Under Standard Normal Curve gives the following area =

0.5 approximately.

So,

P-value = 0.5 - 0.5 nearly =0 nearly

(d)From the information derived, the P-value is less than the significance level.

Therefore, Reject the null hypothesis

In conclusion, there is enough evidence to support the claim that vinyl gloves have a greater virus leak rate than latex gloves.

ur mom

step-by-step explanation:

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.