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Alenkasestr [34]
3 years ago
14

Researchers studying the acquisition of pronunciation often compare measurements made on the recorded speech of adults and child

ren. One variable of interest is called "voice onset time" (VOT), the length of time between the release of a consonant sound (such as "p") and the beginning of an immediately following vowel (such as the "a" in "pat"). For speakers of English, this short time lag can be heard as a period of breathiness between the consonant and the vowel. Here are the results for some randomly selected 4-year-old children and adults asked to pronounce the word "pat". VOT is measured in milliseconds and can be either positive or negative.
Children: n = 10, mean = 60.67, standard deviation = 39.89

Adults: n = 20, mean = 88.17, standard deviation = 24.74

You are interested in whether there is a difference in the VOT of adults and children, so you plan to test H0:μa−μc=0 against Ha:μa−μc≠0, where μa and μcare the population mean VOT for adults and children, respectively.

A. What additional information would you need to confirm that the conditions for this test have been met?

B. Assuming the conditions have been met, calculate the test statistic and p-value for this test.

C. Interpret the p-value in the context of this study and draw the appropriate conclusion at
α = 0.05.

D. Given your conclusion in part C, which type error, Type I or Type II, is it possible to make? Describe that error in the context of this study.
Mathematics
1 answer:
dolphi86 [110]3 years ago
7 0

Answer:

(A) The additional information that is needed to confirm about the conditions for this test have been met is ‘Population is approximately normal.

(B) The test statistic = 1.9965

(C1) P-value = 0.0556

(C2) There is no significant difference between mean VOT for children and adults.

D1) It is possible to make type II error.

(D2) There should be a difference in the VOT of adults and children.

Step-by-step explanation:

Let na be the number of adults = 20

xa mean VOT for adults = 88.17

sa standard deviatiation of VOT for adults = 24.74

Let nc be the number of children = 10

xc mean VOT for children =60.67

sc standard deviatiation of VOT for children = 39.89

(A) From the information the population variances are unknown and the two sample are assumed to be independent and the sample the sample size are smaller that is (n<30).

This indicates that the additional information that is required for the conditions of the test to be satisfied is 'distribution of the population'. the addition assumption to be made is, that the population distribution is normal.

(b) Calculating the test statistics using the formula;

t = (xa -xc)/SE - d

where SE = standard deviation , d= hypothesized difference = 0

But SE = √sa²/na +sc²/nc

           = √24.74 ²/20 + 39.89²/10

           = √189.72559

           = 13.774

Substituting into test statistics equation, we have

t = (xa -xc)/SE - d

  = (88.17 - 60.67/13.774

  = 1.9965

Therefore the test statistic is 1.9965

(c) Calculating the p-value, we have;

Degree of freedom = na + nc -2

                                 = 10+ 20 -2

                                 = 28

The p-value for t=1.9965 at 28 degrees of freedom and 0.05 level of significance is 0.0556.

The p-value 0.0556 is greater than given level of significance 0.05 hence we fail to reject the null hypothesis and conclude that there is no significant difference between mean VOT for children and adults.

(D1) From the information in part (C) the null hypothesis is not rejected.

Since the null hypothesis is not rejected, there might be a chance that not rejecting null hypothesis would be wrong. In this type of situation the error that can occur would be type II error.

(D2) The type of error describe in the context of this study is obtained by the concept of the type II error which tells that the null hypothesis is not rejected when it is actually false.

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juin [17]

Answer:

24,12

Step-by-step explanation:

suppose,

x+y=36

x=2y

2y+y=36

y=12

x=24

4 0
3 years ago
Find the area of the shaded region. With steps
Roman55 [17]

Answer: the area of the shaded region is 72.96 ft²

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Diameter of circle = 16 feet

Radius = diameter/2 = 16/2 = 8 feet

Area of circle = 3.14 × 8² = 200.96ft²

The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

16² = L² + L²

256 = 2L²

L² = 256/2 = 128

L = √128 ft

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L² = (√128)²

Area = 128 ft²

Area of shaded region is

200.96 - 128 = 72.96 ft²

4 0
3 years ago
A bicycle has a listed price of 837.95 before tax if the sales tax rate is 7.5% find the total cost of the bicycle with a sales
Andru [333]

Answer:

The total cost of a bicycle after the tax = $900.8

Step-by-step explanation:

Given

  • The cost of a bicycle before tax = 837.95 (let say in $)
  • Sales tax = 7.5% = 0.075

To determine

The total cost of the bicycle with a sales tax include

The tax amount can be calculated by multiplying Sales tax i.e. 0.075 with the cost of bicycle before tax i.e. 837.95.

Thus,

Tax amount = 7.5% × 837.95

                    = 0.075 × 837.95

                    = $62.85

Thus, the tax amount is: $62.85

Total cost after the tax can be calculated by adding the Tax amount and the cost before tax.

Therefore,

The total cost of a bicycle after the tax = $62.85 + $837.95

                                                                 = $900.8

Hence, the total cost of a bicycle after the tax = $900.8

4 0
2 years ago
Read 2 more answers
Tiffany wants to calculate the volume of her globe. The globe is in the shape of a sphere. She measured the circumference of the
Elis [28]

Answer:

<h2>231in^3</h2>

Step-by-step explanation:

We know that the volume of a sphere/globe is given as

V=4 /3πr^3

but the circumference is expressed as

C=2πr

solving for r given  that C=24

24=2*3.142r

24=6.284r

r=24/6.284

r=3.8in

put r=3.6 in the expression for volume we have

V=4 /3π(3.8)^3

V=4 /3π(55

V=(220.59*3.142)/3

V=693.12/3

V=231in^3

The volume of the globe is 231in^3

3 0
3 years ago
Question #2:
cluponka [151]

Answer:

\$17.59\ per\ hour

Step-by-step explanation:

we know that

The Susan's hourly wage, must be equal at least to the sum of her monthly household expenses divided by the number of hours worked at month

Remember that

1\ year=52\ weeks\\1\ year=12\ months

She works 40 hours  per week

so

40(52)=2,080\ hours\ per\ year

2,080/12=\frac{520}{3}\ hours\ per\ month

<em>Find out the monthly household expenses</em>

Sum all the expenses

Rent+ Monthly Bills+Entertainment and Food+Savings

substitute the values

\$875+\$1,276+\$648+\$250=\$3,049

Find out the hourly wage

\$3,049:\frac{520}{3}\ hours=\$17.59\ per\ hour

3 0
3 years ago
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