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2 years ago

13

A couple plans to have 4 children. Assuming that boys and girls are equally likely, find the probability that the couple will ha

ve at least one boy?

1 answer:

iVinArrow [24]2 years ago

3 0

$A$ - the couple will have at least one boy

$A'$ - the couple will have only girls

$P(A)=1-P(A')$

$|\Omega|=2^4=16\\|A'|=1\\\\P(A')=\dfrac{1}{16}\\\\P(A)=1-\dfrac{1}{16}=\dfrac{15}{16}$

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3 years ago

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3 years ago

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2 years ago

In 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alc

Fynjy0 [20]

Answer:

We conclude that the proportion of adults who totally abstain from alcohol has changed.

Step-by-step explanation:

We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"

Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in

<u><em>Let p = proportion of adults who totally abstain from alcohol.</em></u>

where, p = $\frac{429}{1100}$ = 0.39

So, Null Hypothesis, $H_0$ : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}

Alternate Hypothesis, $H_A$ : p $\neq$ 39% {means that the proportion of adults who totally abstain from alcohol has changed}

The test statistics that would be used here <u>One-sample z proportion statistics</u>;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of adults who totally abstain from alcohol = $\frac{352}{1100}$ = 0.32

n = sample of adults surveyed = 1100

So, <u><em>test statistics</em></u> = $\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }$

= -4.976

The value of z test statistics is -4.976.

<em>Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.</em><em> </em>

<em>Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>

Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.

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3 years ago