What is 105,159 round to the nearest ten thousand is

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and

inn [45]

Complete Question

Polymer composite materials have gained popularity because they have high strength to weight ratios and are relatively easy and inexpensive to manufacture. However, their nondegradable nature has prompted development of environmentally friendly composites using natural materials. An article reported that for a sample of 10 specimens with 2% fiber content, the sample mean tensile strength (MPa) was 51.1 and the sample standard deviation was 1.2. Suppose the true average strength for 0% fibers (pure cellulose) is known to be 48 MPa. Does the data provide compelling evidence for concluding that true average strength for the WSF/cellulose composite exceeds this value? (Use α = 0.05.)

t=8.169

P-value= ?

Answer:

a) $P-value=0$

b) Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.

Step-by-step explanation:

From the question we are told that:

Sample size $n=10$

Mean $\=x= 51.3$

Standard deviation $\sigma=1.2$

Significance level is taken as $\alpha=0.05$

t test statistics

$t=8.169$

Therefore

$P-Value=P(t>8.169)$

Critical point

$t_{\alpha,df}$

$\alpha=0.05$

$df=10-1=>9$

Therefore

P-value from T distribution table

$P-value=0$

Conclusion

$P-value (0)< \alpha(0.05)$

We Reject the Null Hypothesis $H_0$

Hence,We FAil to reject the alternative hypothesis and accept that the true average strength for the WSF/ cellulose composite exceeds 48 MPa.

7 0

3 years ago

What is the value of the following expression if x 22: "five times a number<br> decreased by 2"?

Mila [183]

Answer:

108

Step-by-step explanation:

five times a number x decreased by 2 can be expressed as by 5x- 2

4 0

2 years ago

Suppose a subdivision on the southwest side of Denver, Colorado, contains 1,500 houses. The subdivision was built in 1983. A sam

mihalych1998 [28]

Answer:

0.0268 = 2.68% probability that the sample average is greater than $229,500

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Single house:

The mean appraised value of a house in this subdivision for all houses is $228,000, with a standard deviation of $8,500, which means that $\mu = 228, \sigma = 8.5$