Question

A study was performed on a method of purifying nuclear fuel waste. The process involves oxidation in molten salt and tends to produce oxygen bubbles with a rising velocity. To monitor the process, the researchers collected data on bubble velocity (measured in meters per second) for a random sample of 18 photographic bubble images. These data (simulated) are reproduced in the accompanying table. When oxygen is inserted into the molten salt at a rate (called the sparging rate) of 3.33 x106, the researchers discovered that the true mean bubble rising vocty is H 0.338. Complete parts a and b. 0.265 0.262 0.347 0.222 0.181 0.224 0.318 0.268 0.309 0.274 0.196 0.276 0.268 0.313 0.282 0.304 0.226 0.246 a. Conduct a test of hypothesis to determine if the true mean bubble rising velocity for the population from which the sample is selected is μ-0338. Use α-001. State the null and alternative hypotheses. Choose the correct answer below. А. Но: μ-0.338 Ha: < 0.338 O C. Ho:H 0.338 На: 0.338 В. Но:й-0338 На: μ > 0.338 OD. Но: #0338 На: #0338 Find the test statistic. t-(Round to two decimal places as needed.) Calculate the p-value p-value (Round to three decimal places as needed.)

Please answer the following, thanks!

Answer 1

Solution

Given ,

n = 18 .... sample size

$\alpha$ = 0.01

This sample is as

0.265,0.262,0.347,0.222,0.181,0.224,0.318,0.268,0.309,0.274,0.196,0.276,0.268,0.313,0.282,0.304,0.226,0.246

The hypothesis are

HO: μ = 0.338   (null hypothesis)

H1 : μ $\neq$ 0.338 (alternative hypothesis)

Since the population SD is unknown , we use t distribution.

First we need to find the sample mean $\bar x$ and sample SD s.

$\bar x$=   

sumofobservations

$\bar x$ =   0.2656

Now ,

s=   

I-U z(x - x) 3

Using given data, find Xi-$\bar x$ for each term.take squre for each.then we can easily find s.

s= 0.04408166

Now the test statistic t is given by

t   =

E-H s/n

= (0.2656 - 0.338)/(0.04408166/$\sqrt{}$18)

= -6.97

Now we find p value.

n = 18  $\Rightarrow$ d.f = n - 1 = 17

t_cal = -6.97

Two tailed test

$\therefore$p value = 0.000

p value is less than $\alpha$ .

So, we do reject the null hypothesis.

Option B . There is sufficient evidence at 0.01 level to conclude that the true mean bubble rising velocity is not 0.338 m/s