getarian Child Height Study

GPT-4

User

Researchers studying the effects of diet on growth would like to know if a vegetarian diet affects the height of a child. The researchers randomly selected 14 vegetarian children that were six years old. The average height of the children is 44.5 inches with a standard deviation of 3.8 inches. The average height for all six-year-old children is 47.25 inches. Using confidence intervals, test to determine whether there is overwhelming evidence at a=0.05 that six-year-old vegetanan children are not the same height as other six-year-old children. Assume the population is normally distributed

Step 1 of 2: Calculate a confidence interval for the average height of six-year-old vegetarian children, Round your answers to two decimal places,

Full explanation step by step answer

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To determine whether there is evidence that the average height of six-year-old vegetarian children is different from the overall average height of all six-year-olds, we can use a confidence interval approach. We'll use a

95

%

95% confidence interval (since

�

=

0.05

α=0.05).

Step 1 of 2: Calculate the

95

%

95% confidence interval for the average height of six-year-old vegetarian children.

Given:

Sample size

�

=

14

n=14

Sample mean

�

ˉ

=

44.5

x

ˉ

=44.5 inches

Sample standard deviation

�

=

3.8

s=3.8 inches

Significance level

�

=

0.05

α=0.05

First, we need to find the t-value from the t-distribution for a

95

%

95% confidence interval with

�

−

1

=

13

n−1=13 degrees of freedom. You can use a t-table or statistical software to find this value.

Using a t-table for

�

/

2

=

0.025

α/2=0.025 (two-tailed) and

�

�

=

13

df=13, the t-value is approximately

2.160

2.160.

Next, calculate the margin of error (MOE) using the formula:

�

�

�

=

�

×

(

�

�

)

MOE=t×(

n

s

)

�

�

�

=

2.160

×

(

3.8

14

)

MOE=2.160×(

14

3.8

)

�

�

�

≈

2.160

×

1.015

MOE≈2.160×1.015

�

�

�

≈

2.19

MOE≈2.19

Now, we can calculate the

95

%

95% confidence interval:

�

ˉ

−

�

�

�

to

�

ˉ

+

�

�

�

x

ˉ

−MOE to

x

ˉ

+MOE

44.5

−

2.19

to

44.5

+

2.19

44.5−2.19 to 44.5+2.19

42.31

to

46.69

42.31 to 46.69

So, the

95

%

95% confidence interval for the average height of six-year-old vegetarian children is

(

42.31

,

46.69

)

(42.31,46.69) inches.

The average height for all six-year-old children is 47.25 inches. Since 47.25 is outside the confidence interval, there is evidence at the

�

=

0.05

α=0.05 level to conclude that the average height of six-year-old vegetarian children is different from that of all six-year-old children. We'll further assess this evidence in the next step.

User

factorise 3 root 3 x power 3 minus 5 root 5 Y power 3

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To factorise the expression:

3

3

�

3

−

5

5

�

3

3

3

x

3

−5

5

y

3

We can use the difference of cubes formula:

�

3

−

�

3

=

(

�

−

�

)

(

�

2

+

�

�

+

�

2

)

a

3

−b

3

=(a−b)(a

2

+ab+b

2

)

To apply this formula, we need to express each term as a cube:

(

3

3

3

�

)

3

−

(

5

5

3

�

)

3

(

3

3

3

x)

3

−(

3

5

5

y)

3

Here:

�

=

3

3

3

�

a=

3

3

3

x

�

=

5

5

3

�

b=

3

5

5

y

Now, let's apply the difference of cubes formula:

�

3

−

�

3

=

(

�

−

�

)

(

�

2

+

�

�

+

�

2

)

a

3

−b

3

=(a−b)(a

2

+ab+b

2

)

3

3

�

3

−

5

5

�

3

3

3

x

3

−5

5

y

3

=

(

3

3

3

�

−

5

5

3

�

)

[

(

3

3

3

�

)

2

+

(

3

3

3

�

)

(

5

5

3

�

)

+

(

5

5

3

�

)

2

]

=(

3

3

3

x−

3

5

5

y)[(

3

3

3

x)

2

+(

3

3

3

x)(

3

5

5

y)+(

3

5

5

y)

2

]

The expression is now factored, but expanding and simplifying the resulting polynomial can be quite complex. For many purposes, it might be sufficient to leave the factorization in this form.

User

एक पिता ने अपनी पुत्री के लिए बाग से दो अमरूद तोड़े। पुत्री ने एक-एक अमरूद अपने दोनों हाथों में ले लिए। पिता ने एक अमरूद माँगा, तो बेटी ने बारी-बारी दोनों अमरूदों में से एक-एक टुकड़ा दाँतों से काट लिया। पिता को उसके लालच पर बहुत अफ़सोस हुआ। इतने में पुत्री ने अपने पिता को एक अमरूद देते हुए कहा कि आप इसे खाइए यह मीठा है। पिता को अपने संकुचित विचारों पर बहुत पश्चाताप हुआ।

Answer:-

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उपर्युक्त कहानी एक बहुत ही संवेदनशील और अद्वितीय संदेश प्रस्तुत करती है। इसमें पिता अपनी बेटी के प्रति उसकी स्वार्थभावना को देखकर निराश होते हैं, लेकिन बेटी के अगले कदम और उसकी अद्वितीय भावना को देखकर उन्हें समझ में आता है कि उन्होंने बेटी की भावनाओं को समझने में गलती की है। बेटी ने सिर्फ यह सुनिश्चित करना चाहा था कि वह अपने पिता को मीठा अमरूद ही दे। इस कहानी का मुख्य संदेश यह है कि हमें किसी की भी भावनाओं और कार्यों को उसकी सतही दिखाई देने वाली स्थिति में ही मूल्यांकन नहीं करना चाहिए। हमें समझना चाहिए कि हर व्यक्ति के प्रत्येक कार्य के पीछे एक अदृश्य संवेदनशीलता होती है, जिसे हमें समझने की कोशिश करनी चाहिए।