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9966 [12]
3 years ago
10

A 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selecti

on, the proportion of baby girls is greater than 0.5. Assume that sample data consists of 78 girls in 144 ​births, so the sample statistic of StartFraction 13 Over 24 EndFraction results in a z score that is 1 standard deviation above 0. Complete parts​ (a) through​ (h) below.
(a) Identify the null hypothesis and the alternative hypothesis. Choose the correct answer below.
a. H0:p=0.5 H1:P≠0.5.
b. H0:p≠0.5 H1:p=0.5.
c. H0:p=0.5 H1:p>0.5.
d. H0:p=0.5 H1:p<0.5.
(b) What is the value of α? (Type an integer or a decimal.)
(c) What is the sampling distribution of the sample statistic?
a. Normal distribution.
b. χ2.
c. Student (t) distribution.
(d) Is the test two-tailed, left-tailed, or right-tailed?
a. Right-tailed.
b. Left-tailed.
c. Two-tailed.
(e) What is the value of the test statistic? (Type an integer or a decimal).
(f) What is the P-value? (Round to four decimal places as needed.)
(g) What are the critical values(s)? (Round to three decimal places as needed. Use a comma to separate answers as needed.)
(h) What is the area of the critical region? (Round to two decimal places as needed.)
Mathematics
1 answer:
Andrews [41]3 years ago
7 0

Answer:

(a) Null Hypothesis, H_0 : p = 0.50

    Alternate Hypothesis, H_A : p > 0.50

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed.

(e) The value of z test statistics is 0.96.

(f) The P-value is 0.1685.

(g) At 0.10 significance level the z table gives critical value of 1.282 for right-tailed test.

(h) We conclude that the proportion of baby girls is equal to 0.50.

Step-by-step explanation:

We are given that a 0.1 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is greater than 0.5.

Assume that sample data consists of 78 girls in 144 ​births.

Let p = <u><em>population proportion of baby girls</em></u>

(a) So, Null Hypothesis, H_0 : p = 0.50     {means that the proportion of baby girls is equal to 0.50}

Alternate Hypothesis, H_A : p > 0.50     {means that the proportion of baby girls is greater than 0.50}

(b) The value of level of significance (α) given in the question is 0.10.

(c) The sampling distribution of the sample statistic is Normal distribution.

(d) This test is right-tailed as in the alternative hypothesis we are concerned for proportion of baby girls that is greater than 0.50.

(e) The test statistics that would be used here <u>One-sample z test for proportions</u>;

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

where, \hat p = sample proportion of baby girls =  \frac{78}{144} = 0.54

            n = sample of births = 144

So, <u><em>the test statistics</em></u>  =  \frac{0.54-0.50}{\sqrt{\frac{0.54(1-0.54)}{144} } }  

                                       =  0.96

The value of z test statistics is 0.96.

(f) <u>The P-value of the test statistics is given by;</u>

            P-value = P(Z > 0.96) = 1 - P(Z < 0.96)

                          = 1 - 0.8315 = 0.1685

<u></u>

(g) <u>Now, at 0.10 significance level the z table gives critical value of 1.282 for right-tailed test.</u>

(h) Since our test statistic is less than the critical value of z as 0.96 < 1.282, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region (which was to the right of value of 1.282) due to which <u>we fail to reject our null hypothesis</u>.

Therefore, we conclude that the proportion of baby girls is equal to 0.50.

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No copy and paste answers.
miss Akunina [59]

Answer:

  2.5 miles

Step-by-step explanation:

The relation between time, speed, and distance is ...

  distance = speed × time

We can define t to be Stanley's swimming time. Then t+0.5 was his running time, and 2(t+0.5) was his biking time. His total distance covered is ...

  64 = 9(t +0.5) +16(2(t +0.5)) +2.5(t)

  64 = 43.5t +20.5 . . . . . . . simplify

  43.5 = 43.5t . . . . . . . . . subtract 20.5

  t = 1 . . . . . . . . . . . . . . divide by the coefficient of t

Stanley swam for 1 hour, so the distance he covered while swimming was ...

  (2.5 mi/h)(1 h) = 2.5 mi

Stanley covered 2.5 miles while swimming.

_____

<em>Additional comment</em>

Stanley ran for 1.5 hours, covering 9×1.5 = 13.5 miles. He biked for 3 hours, covering 16×3 = 48 miles. His total distance was 2.5 +13.5 +48 = 64 miles, as given.

6 0
2 years ago
Monyne Phillips three coins. What is the probability that the first second and third Cornwall in the same way (either all heads
nasty-shy [4]

Answer:

1 in 8 chance.

Step-by-step explanation:

When a coin flips is has two outcomes: heads or tails, obviously.

Whenever you have a 50/50 probability, in this case a coin, every time you add another coin the amount of outcomes squares, or multiplies by the number of outcomes, and since we are using a coin, two. To reiterate, say we were using a die, a die is a cube, a six sided shape, so there are six outcomes. The chances of getting all sixes with one die is 1 in 6. Add another die and try to get all sixes, the chances become 1 in 36. We got this by multiplying our out comes by our outcomes

1 coin: 2 outcomes

2 coins: 4 outcomes

3 coins: 8 outcomes

Another thing:

Don't be fooled by questions being specific by saying "all heads" or "all tails"...

This is a wording trick, no matter the outcome, the chances will always be equal.

Good luck :)

8 0
3 years ago
Jill collected a total of 19 gallons of honey. If she distributed all of the honey equally between 9 jars how much will be in ea
Ratling [72]
There would be 2g in each jar
8 0
3 years ago
Please help me with the work because i dont understand this.
Alexandra [31]

Answer:

The dimension are 20 ft by 15 ft

Step-by-step explanation:

A = l*w

P = 2(l+w)

we know the area = 300

and the perimeter = 70

300 = lw

70 = 2 (l+w)

divide by 2

70/2 = 2/2 (l+w)

35 = l+w

subtract w

35-w = l+w-w

35 -w =l

substitute this into 300 = lw

300 = (35-w) * w

distribute

300 = 35w - w^2

subtract 300 from each side

0 = -w^2 +35w - 300

divide by -1

0 = w^2 - 35w + 300

factor

0= (w-15) (w-20)

using the zero product property

w-15 = 0   w-20 =0

so w=15, w=20

if w=15   then l=35 -w  l = 35-15   l=20

if w=20  then l=35-w   l= 35-20 = 15


The dimension are 20 ft by 15 ft

7 0
3 years ago
4/3 + -1/6 + 13/12. Please answer step by step if possible. Thanks.
strojnjashka [21]

Answer:

9/4

Step-by-step explanation:

We follow bodmas

4/3 +( -1/6 + 13/12)

( lcm = 12)

( -2+ 13/12)

( 11/ 12)

4/3 + ( 11/12)

4/3 + 11/12

lcm = 12 also

and that will equal to

=16 + 11/ 12

= 27/ 12

divide by 3 to simplest form

= 9/4

6 0
2 years ago
Read 2 more answers
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