1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
frosja888 [35]
3 years ago
7

Inspired by zoom, you want to determine whether there are significant differences in the satisfaction of couples that had their

first date in person vs. couples who had their first date virtually. Based on the following satisfaction data (larger values indicate greater satisfaction), conduct an independent samples t-test using (alpha=.01) and an pooled variance. Is there a significant difference?
Virtual Date In person date
X= 23.76 X= 34.54
s2 = 123.43 s2 = 105.65
n = 5 n = 20
A) Write the null and alternative hypotheses in symbols
B) What is your critical value?
C) What's your pooled variance?
D) What's your standard error?
E) What's your obtained t?
Mathematics
1 answer:
zalisa [80]3 years ago
7 0

Answer:

A) The null hypothesis is H₀; \overline x_1 = \overline x_2

The alternative hypothesis is Hₐ; \overline x_1 ≠ \overline x_2

B) The critical value is 4.604

C) The pooled variance is 11,870.2777

D) The standard error is-0.2321

E) The obtained is -0.2040  

Step-by-step explanation:

The given values are;

\overline x_1 = 23.76, \overline x_2 = 34.54

s₁ = 123.43, s₂ = 105.65

n₁ = 5, n₂ = 20

A) The null hypothesis, H₀; \overline x_1 = \overline x_2

The alternative hypothesis, Hₐ; \overline x_1 ≠ \overline x_2

B) The degrees of freedom, df = 4 - 1 = 3

The critical t-value is given at α = 0.01 is given on the t-table for two tailed test as t = 4.604

C) The pooled variance is given by the following formula;

S_P^2 = \dfrac{(n_1 - 1) \cdot s_1^2 + (n_2-1) \cdot s_2^2}{n_1 + n_2 - 2 }

Plugging in the values gives;

S_P^2 = \dfrac{(5 - 1) \cdot 123.43^2 + (20-1) \cdot 105.65^2}{5+ 20 - 2 } = 11,870.2777

The pooled variance, s_p^2 = 11,870.2777

D) The standard error, SE, is given as follows;

t=\dfrac{(\bar x_{1}-\bar x_{2})}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}

Therefore, we get;

t=\dfrac{(23.76-35.34)}{\sqrt{\dfrac{123.43^{2} }{5}-\dfrac{105.65^{2}}{20}}} = -0.2321

The standard error, SE ≈ -0.2321

E) The obtained 't' is given as follows;

\sigma _{\overline x_1 - \overline x_2} = \sqrt{\dfrac{s_1^2}{n_1-1} +\dfrac{s_2^2}{n_2-1} }

Therefore, we have;

\sigma _{\overline x_1 - \overline x_2} = \sqrt{\dfrac{123.43^2}{5-1} +\dfrac{105.65^2}{20-1} } \approx 56.7564

The obtained t is given as follows;

t(Obtained)=\dfrac{(\bar x_{1}-\bar x_{2})}{\sigma _{\overline x_1 - \overline x_2} }

Therefore, we get;

t(Obtained)=\dfrac{(23.76-34.54)}{56.7564} \approx -0.2040

The obtained t = -0.2040

You might be interested in
The number of boys in a club is 10 more than half the number of girls.
Sav [38]

Answer:

40 girls

Step By Step Explanation:

assume boys = y girls = x

y = 1/2x + 10

y = 30

30 = 1/2x + 10

1/2x = 20  

x = 20 *2 = 40

girls is  40   boys is 30

6 0
3 years ago
Please Help Me : ]
Goryan [66]

Answer:

b

Step-by-step explanation:

the anwser to this question is b i think

5 0
3 years ago
The slope of the line is -3. Use the coordinates of the labeled point to find the point-slope equation of the line.
nekit [7.7K]
m =  \dfrac{Y_2 - Y_1}{X_2-X_1}

-3 =  \dfrac{y + 7}{x - 5}

y + 7= -3(x - 5)

Answer A

8 0
3 years ago
Read 2 more answers
Question.<br> А<br> 0<br> 2<br> 3<br> Which fraction does point A show?<br> A<br> B<br> C<br> D
Alex787 [66]

Answer:

B

Step-by-step explanation:

I don't remember but I just know how to do it

4 0
3 years ago
Writing in Math Describe a situation in which it would be better
NeTakaya

Answer:

the number 151

Step-by-step explanation:

this because if you round 151 to the nearest hundread it would give you 200 but if you round it to the nearest ten ot would give you 150 which is closer to the actual number than 200.

5 0
3 years ago
Other questions:
  • The diameter of a certain ball is 2.9 inches. What is the volume of the ball? (Round your answer to two decimal places.) in The
    7·1 answer
  • The sum of four times a number and five times another number is -28. The sum of nine times the first number and two times the se
    9·1 answer
  • How many ways can 11 basketball players and their coach (12 people in total) be
    5·1 answer
  • List the the single -digits factor of 924.
    12·1 answer
  • -7x-13&gt;_8 as a number line
    9·2 answers
  • Simplify the following expression by combining like terms 6y-23-y+72
    9·1 answer
  • One number is 10 more than another number. If the product of the two numbers is -21 find both numbers
    13·1 answer
  • I need help now pls
    11·1 answer
  • Use a t-distribution to answer this question. Assume the samples are random samples from distributions that are reasonably norma
    8·1 answer
  • Choose 5 ordered pairs whose second component is the opposite of the first component.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!