Challenge 1:

You are buying a $50 video game as a holiday gift for your brother luckily you have not just one but two coupons for that store

postnew [5]

Whats the question though?

6 0

4 years ago

A new post-surgical treatment is being compared with a standard treatment. Seven subjects receive the new treatment, while seven

AnnyKZ [126]

Answer:

$t=\frac{17.71-28.71}{\sqrt{\frac{4.461^2}{7}+\frac{7.387^2}{7}}}}=-3.372$

$df=n_{S}+n_{N}-2=7+7-2=12$

Since is a one sided test the p value would be:

$p_v =P(t_{(12)}$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean time for the new treatment is significantly lower than the time for the standard treatment at 5% of significance.

Step-by-step explanation:

New: 12, 13,15,19,20,21

Standard: 18,23,24,30,32,35

We can calculate the sample mean and deviation with the following formulas:

$\bar X = \frac{\sum_{i=1}^n X_i}{n}$

$s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}$

Data given and notation

$\bar X_{N}=17.71$ represent the mean for the new case

$\bar X_{S}=28.71$ represent the mean for the standard case

$s_{N}=4.461$ represent the sample standard deviation for the new case

$s_{S}=7.387$ represent the sample standard deviation for the standard case

$n_{S}=7$ sample size selected for the standard case

$n_{N}=7$ sample size selected for the new case

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if recovery time for patients who receive the new treatment is less than the mean for patients who receive the standard treatment, the system of hypothesis would be:

Null hypothesis: $\mu_{N} \geq \mu_{S}$

Alternative hypothesis: $\mu_{N} < \mu_{S}$

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{N}-\bar X_{S}}{\sqrt{\frac{s^2_{N}}{n_{N}}+\frac{s^2_{S}}{n_{S}}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{17.71-28.71}{\sqrt{\frac{4.461^2}{7}+\frac{7.387^2}{7}}}}=-3.372$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n_{S}+n_{N}-2=7+7-2=12$

Since is a one sided test the p value would be:

$p_v =P(t_{(12)}$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the mean time for the new treatment is significantly lower than the time for the standard treatment at 5% of significance.

6 0

4 years ago

Julie is a math tutor. She charges each student $210 for the first 7 hours of tutoring and $20 for each additional hour. When th

Nady [450]

A = 210 + 20(h - 7) <== ur equation

if she earns 410 tutoring...
410 = 210 + 20(h - 7)
410 = 210 + 20h - 140
410 = 20h + 70
410 - 70 = 20h
340 = 20h
340/20 = h
17 = h <=== she spent 17 hrs tutoring

8 0

3 years ago

The voltage in a circuit is the product of two factors, the resistance and the current. If the voltage is 6ir + 15i + 8r+20, fin

Alenkinab [10]

Answer:

resistance: (2r +5)
current: (3i +4)

Step-by-step explanation:

The factors of the given expression are ...

6ir +15i +8r +20 = (3i +4)(2r +5)

Which factor is current and which is resistance is not clear. Usually, resistance is referred to using the variable r, so we suppose the expressions are supposed to be ...

resistance: (2r +5)

current: (3i +4)

8 0

3 years ago

The diameter of a circle is 9 centimeters. Find the area to the nearest tenth.

Umnica [9.8K]

Answer:

63.6 square cm

Step-by-step explanation:

$d = 9 \: cm \implies \: r = 4.5 \: cm \\ area \: of \: circle \\ = \pi {r}^{2} \\ = 3.14 \times ( {4.5})^{2} \\ = 3.14 \times 20.25 \\ = 63.585 \\ = 63.6 \: {cm}^{2} \\$

8 0

3 years ago