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Alexxandr [17]
2 years ago
11

The table represents the height of a rock that is dropped, h(t), in meters, after t seconds. (See picture.)

Mathematics
2 answers:
hjlf2 years ago
6 0

Answer:

2,2.5

Step-by-step explanation:

Misha Larkins [42]2 years ago
3 0

Answer: Between <u>2</u> and <u>2.5</u> seconds

How am I getting those values? Those values are selected from the 't' column on the left side of the table. These are time values in seconds. Note how t = 2 corresponds to h = 0.4; while t = 2.5 corresponds to h = -10.6

The change in sign for the height, from positive to negative, means that the height h must be zero at some point between t = 2 seconds and t = 2.5 seconds. We don't know where exactly, but we know that h = 0 at least once in this interval. This is because the height is a continuous function. There are no jumps or gaps in the height (the object can't teleport or anything)

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t=\frac{25000-210000}{\frac{37500}{\sqrt{5}}}=2.37  

p_v =P(t_{4}>2.37)=0.038  

If we compare the p value and a significance level assumed \alpha=0.1 we see that p_v so we can conclude that we reject the null hypothesis, and the actual true mean is higher than 210250 at 5% of significance.  

Step-by-step explanation:

Data given and notation

\bar X=250000 represent the sample mean  

s=37500 represent the standard deviation for the sample

n=5 sample size  

\mu_o =210250 represent the value that we want to test  

\alpha=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 to be tested  

We need to conduct a hypothesis in order to determine if the mean is higher than 210250, the system of hypothesis would be:  

Null hypothesis:\mu \leq 210250  

Alternative hypothesis:\mu > 210250  

Compute the test statistic  

We don't know the population deviation, so for this case 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".  

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

t=\frac{25000-210000}{\frac{37500}{\sqrt{5}}}=2.37  

Now we need to find the degrees of freedom for the t distirbution given by:

df=n-1=5-1=4

Conclusion

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

p_v =P(t_{4}>2.37)=0.038  

If we compare the p value and a significance level assumed \alpha=0.1 we see that p_v so we can conclude that we reject the null hypothesis, and the actual true mean is higher than 210250 at 5% of significance.  

6 0
3 years ago
A professor at a local university noted that the exam grades of her students were normally distributed with a mean of 73 and a s
jasenka [17]

Answer:

The minimum score of those who received C's is 67.39.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 73, \sigma = 11

If 69.5 percent of the students received grades of C or better, what is the minimum score of those who received C's?

This is X when Z has a pvalue of 1-0.695 = 0.305. So it is X when Z = -0.51.

Z = \frac{X - \mu}{\sigma}

-0.51 = \frac{X - 73}{11}

X - 73 = -0.51*11

X = 67.39

The minimum score of those who received C's is 67.39.

7 0
3 years ago
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