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Consider the following hypothesis test:H 0: = 17H a: 17A sample of 40 provided a sample mean of 14.12. The population standard deviation is 4.a. Compute the value of the test statistic (to 2 decimals). (If answer is negative, use minus "-" sign.)b. What is the p-value (to 4 decimals)?c. Using = .05, can it be concluded that the population mean is not equal to 17? SelectYesNoItem 3Answer the next three questions using the critical value approach.d. Using = .05, what are the critical values for the test statistic (to 2 decimals)? ±e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 5 the lower critical value and is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal toItem 6 the upper critical value.f. Can it be concluded that the population mean is not equal to 17?

Answers

Answer 1

Answer:

Answer:

We conclude that the population mean is not equal to 17.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 17

Sample mean, $\bar{x}$ = 14.12

Sample size, n = 40

Alpha, α = 0.05

Population standard deviation, σ = 4

First, we design the null and the alternate hypothesis

$H_(0): \mu = 17\nH_A: \mu \neq 17$

We use Two-tailed z test to perform this hypothesis.

a) Formula:

$z_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n)) }$

Putting all the values, we have

$z_(stat) = \displaystyle(14.12 - 17)/((4)/(√(40)) ) = -4.5536$

b) P-value can be calculated from the standard z-table.

P-value = 0.0000

c) Since the p-value is less than the significance level, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17

d) Now, $z_(critical) \text{ at 0.05 level of significance } = \pm 1.96$

e) Rejection Rule:

We reject the null hypothesis if it is less than lower critical value and greater than the upper critical value

If the z-statistic lies outside the acceptance region which is from -1.96 to +1.96, we reject the null hypothesis.

f) Since the calculated z-stat lies outside the acceptance region, we reject the null hypothesis and accept the alternate hypothesis. Thus, the population mean is not equal to 17.

Answer 2

Answer:

Final answer:

The test statistic is -1.78 and the p-value is 0.0761, indicating that we fail to reject the null hypothesis. Therefore, it cannot be concluded that the population mean is not equal to 17.

Explanation:

The test statistic can be calculated using the formula:

test statistic = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Plugging in the given values, we get:

test statistic = (14.12 - 17) / (4 / sqrt(40))

Calculating this gives us a test statistic value of -1.78.

The p-value can be calculated using the test statistic. We need to find the probability that a test statistic at least as extreme as -1.78 would occur assuming the null hypothesis is true. Using a standard normal distribution table or software, we find the p-value to be approximately 0.0761.

Since the p-value is greater than the significance level (alpha = 0.05), we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the population mean is not equal to 17.

Learn more about Hypothesis testing here:

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Please help me on this

Will wanted to track the growth of various fruits in his garden, so he decided to label them. His garden had APPLES labeled 1,2,3,4,5,6, LEMONS labeled 1,2, and MELONS labeled 1,2,3. If a single fruit is picked at random, what is the probability that the fruit is an APPLE or has an EVEN number?

Answers

Using the probability concept, it is found that there is a 0.7273 = 72.73% probability that the fruit is an APPLE or has an EVEN number.

A probability is the number of desired outcomes divided by the number of total outcomes.

In this problem:

There are 11 options, hence $T = 11$ .
Of those, there are 6 options which land on Apple, plus 2 options which does not land on apple but have an even number, hence $D = 6 + 2 = 8$

Then, the probability is:

$p = (D)/(T) = (8)/(11) = 0.7273$

0.7273 = 72.73% probability that the fruit is an APPLE or has an EVEN number.

A similar problem involving the probability concept is given at brainly.com/question/15536019

Answer:

8 in 11 or 0.7272

Step-by-step explanation:

Between 6 apples. 2 lemons and 3 melons, Will has a total of 11 fruits in his garden. There are three apples labeled with even numbers (2,4 and 6), one melon (2) and one lemon (2), for a total of five fruits.

The probability that a randomly selected fruit is an APPLE or has an EVEN number is given by the probability that it is an apple, P(A), added to the probability that it is even, P(E), minus the probability that it is an even apple, P(A and E):

$P(A\ or\ E) = P(A) +P(E) - P(A\ and\ E)\nP(A\ or\ E) = (6)/(11)+(5)/(11)-(3)/(11) \nP(A\ or\ E) = 0.7272$

There is a 8 in 11, or a 0.7272 chance that the fruit is an APPLE or has an EVEN number.

The number line below represents which combined inequality?number line with a closed circle on negative 4 and 3 with shading in between

x greater than or equal to −4 and x less than or equal to 3
x greater than or equal to −4 or x less than or equal to 3
x less than or equal to −4 and x greater than or equal to 3
x less than or equal to −4 or x greater than or equal to 3

Answers

x greater than or equal to −4 and x less than or equal to 3

This is because of the fact that it is in between.

Answer:

Step-by-step explanation:

X greater or equal to -4 and X less than or equal to 3

Answer number one

A town interested in installing wind turbines to generate electricity measures the speed of the wind in the town over the course of a year. They find that most of the time, the wind speed is pretty slow, while only rarely does the wind blow very fast during a storm. What would be the best measure of the central wind speed they should report to the mayor? The mean, because the distribution of wind speeds is skewed. The median, because the distribution of wind speeds is symmetric. The mean, because the distribution of wind speeds is symmetric. The median, because the distribution of wind speeds is skewed. The proportion, because the distribution of wind speeds is skewed. The proportion, because the distribution of wind speeds is symmetric.

Answers

9514 1404 393

Answer:

The median, because the distribution of wind speeds is skewed.

Step-by-step explanation:

A few higher speeds will raise the mean. For a skewed distribution, the median may be a more appropriate measure of center.

Additional comment

From an engineering point of view, one might have to consider speeds only within some range, as the wind turbines may be shut down for speeds too low or too high. Likely the power generated is not proportional to speed, so a weighted average (of the square of speed) would probably be more useful. Unfortunately, this question does not get into such subtleties.

Solve the equation for the value of x-6=x/-4

Please show your work, thank you.

Answers

Answer: x=24

x=-6*-4=24

If 10 people apply for 3 jobs in how many ways can people be chosen for the jobs. 1. If the jobs are all the same. 2. If the jobs are all different. (please, please show work! Thank you!)