3. A child psychologist asked 100 five year olds and 50 ten year olds to name their favorite

Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? The ar

snow_tiger [21]

Answer:

Yes. There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.

Step-by-step explanation:

The sample of the remaining toothpaste is: [.53, .65, .46, .50, .37].

This sample has a size n=5, a mean M=0.502 and standard deviation s=0.102.

$M=\dfrac{1}{5}\sum_{i=1}^{5}(0.53+0.65+0.46+0.5+0.37)\\\\\\ M=\dfrac{2.51}{5}=0.502$

$s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.53-(0.502))^2+...+(0.37-(0.502))^2]}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.001)+(0.022)+(0.002)+(0)+(0.017)]}\\\\\\ s=\sqrt{\dfrac{0.04188}{4}}=\sqrt{0.01047}\\\\\\s=0.102$

The 10% of the advertised content is:

$0.10\cdot 6.0\;oz=0.6\:oz$

Hypothesis test for the population mean:

The claim is that the remaining toothpaste is significantly is less than 10% of the advertised net content.

Then, the null and alternative hypothesis are:

$H_0: \mu=0.6\\\\H_a:\mu< 0.6$

The significance level is 0.05.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.102}{\sqrt{5}}=0.046$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.502-0.6}{0.046}=\dfrac{-0.098}{0.046}=-2.148$

The degrees of freedom for this sample size are:

$df=n-1=5-1=4$

This test is a left-tailed test, with 4 degrees of freedom and t=-2.148, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.049) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.

7 0

3 years ago

A wedding website states that the average cost of a wedding is $25,809. One concerned bride hopes that the average is less than

lapo4ka [179]

Answer:

1)

Null hypothesis H₀ : μ = 25,809

Alternative hypothesis H₁ : μ < 25,809

2) Test Statistic = -1.44

3) Conclusion:

The result is significant, there is sufficient evidence to support the bride’s hope at the 0.10 level of significance.

Step-by-step explanation:

Given the data in the question;

Sample mean x" = 24,638

sample size n = 46

standard deviation σ = 5531

level of significance ∝ = 0.10

NULL and ALTERNATIVE HYPOTHESIS

Null hypothesis H₀ : μ = 25,809

Alternative hypothesis H₁ : μ < 25,809

TEST STATISTICS

Z = (x"-μ) / σ√n

we substitute

Z = (24,638 - 25,809) / (5531/√46)

Z = -1171 / 815.5

Z = -1.44

Test Statistic = -1.44

Now, from normal z-table;

P-value = P( Z < -1.44 ) = 0.0749

P-value = 0.0749

Since P-value ( 0.0749 ) is less than level of significance ( 0.10 ), we reject H₀.

Conclusion:

The result is significant, there is sufficient evidence to support the bride’s hope at the 0.10 level of significance.

6 0

2 years ago

The half life of a certain tranquilizer in the bloodstream is 37 hours. How long will it take for the drug to decay to 86% of th

nata0808 [166]

Answer:

8.1 hours

Step-by-step explanation:

A model of the fraction remaining can be ...

f = (1/2)^(t/37) . . . . t in hours

So, for the fraction remaining being 86%, we can solve for t using ...

0.86 = 0.5^(t/37)

log(0.86) = (t/37)log(0.5)

t = 37·log(0.86)/log(0.5) ≈ 8.0509 ≈ 8.1 . . . hours

It takes about 8.1 hours to decay to 86% of the original concentration.

5 0

2 years ago

A father lifts a toddler 1.5 m up in the air. The child gains 187.5 J of energy in her gravitational potential energy store as a

bearhunter [10]

The mass of the toddler is 12.5 kg.

Step-by-step explanation:

The equation for gravitational potential energy is Ep=mgh where;

Ep=gravitational potential energy

m=mass of an object

g=gravitational field strength

h=height in meters

Given that ; h= 1.5m, Ep=187.5J , g=10 N/kg then finding m;

Ep=mgh

187.5=m*10*1.5

187.5=15m

187.5/15 =15m/15

12.5 kg=m

Learn More

Gravitation potential energy : brainly.com/question/939365

Keyword : Mass, gravitational potential energy

#LearnwithBrainly

5 0

2 years ago

A company contracts to paint 3 houses. Mr. Brown can paint a house in 6 days while Black would take 8 days and Blue 12 days. Aft

AleksAgata [21]

You can start with the equation of
(1/6)x8+(1/8)x6+(1/12)x X=3

Multiply by common denominator of 24 to get
32+18+2x=72

Simplify it we get
50+2x=72

Eliminate using algebra (because it’s add 50 take away the 50 on both sides)
2x=22

Because it’s X2 divide by 2 on both sides
x=11
It will take 11 days

6 0

2 years ago