Write an equation to show the best way to estimate 208 ÷ 7 using compatible numbers

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has b

baherus [9]

Answer:

Null hypothesis: $\mu \leq 6$

Alternative hypothesis: $\mu > 6$

$t=\frac{6.5-6}{\frac{1.5}{\sqrt{36}}}=2$

$df=n-1=36-1=35$

$t_{crit}=1.690$ with the excel code:"=T.INV(0.95,35)"

$t_{crit}=1.306$ with the excel code:"=T.INV(0.90,35)"

$p_v =P(t_{(35)}>2)=0.0267$

If we compare the p value and the significance level given $\alpha=0.05,0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the true mean it's significantly higher than 6 at 5% and 10% of significance.

Step-by-step explanation:

Data given and notation

$\bar X=6.5$ represent the mean time for the sample

$s=1.5$ represent the sample standard deviation for the sample

$n=36$ sample size

$\mu_o =6$ represent the value that we want to test

$\alpha=0.05,0.1$ 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 the mean is higher than 6 days, the system of hypothesis would be:

Null hypothesis: $\mu \leq 6$

Alternative hypothesis: $\mu > 6$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

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

$t=\frac{6.5-6}{\frac{1.5}{\sqrt{36}}}=2$

Critical value and P-value

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

$df=n-1=36-1=35$

In order to calculate the critical value we need to find a quantile on the t distribution with 35 degrees of freedom that accumulates $\alpha$ on the right. Using the significance level of 0.05 we got:

$t_{crit}=1.690$ with the excel code:"=T.INV(0.95,35)"

And using the significance of 0.1 we got

$t_{crit}=1.306$ with the excel code:"=T.INV(0.90,35)"

Since is a one side right tailed test the p value would be:

$p_v =P(t_{(35)}>2)=0.0267$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05,0.1$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the true mean it's significantly higher than 6 at 5% and 10% of significance.

6 0

3 years ago

2. A(n) _______________ system is a system of equations with an infinite number of solutions.

Anna11 [10]

Answer:

If a system has infinitely many solutions, then the lines overlap at every point. In other words, they're the same exact line! This means that any point on the line is a solution to the system. Thus, the system of equations above has infinitely many solutions.

Step-by-step explanation:

4 0

3 years ago

your chocolate milk mix says to use 4 scoops of mix for 2 cups of milk. after pouring in the milk, you start adding the mix, but

postnew [5]

Add a half a cup of milk. Enjoy your chocolate milk!!!

5 0

3 years ago

Triangle XYZ has vertices X(1, 3), Y(0, 0), and Z(–1, 2). The image of triangle XYZ after a rotation has vertices X'(–3, 1), Y'(

emmainna [20.7K]