A newspaper published an article about a study in which researchers subjected laboratory gloves to stress. Among 279 vinyl gloves, 60% leake

Question

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

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Eloise 3 months 2022-02-05T16:00:17+00:00 1 Answer 0 views 0

Answers ( )

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    2022-02-05T16:01:28+00:00

    Answer:

    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.

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