Please show work and formula, I need help with number 4, 6, and 7 A random sample of 25 frozen dinners of a certain type was selected from production during a particular period and the calorie content of each one was determined. The resulting observations are: Calories from Frozen Dinners 255 244 239 242 265 245 259 248 225 226 251 233 266 227 246 240 257 222 237 270 230 260 268 231 238 The stated calorie content is 240 calories. At the 5% significance level, do the data suggest that the mean calorie content of the frozen dinners differs from 240 calories? State the null and alternative hypothesis Check the conditions. To determine if the data is approximately normal, using paper and pencil methods, construct a histogram. If the conditions have not been satisfied, still continue with the assignment. State the significance level. and then draw and fully label the rejection regions. Calculate the test statistic and p-value. You may use the calculator to calculate the mean and standard deviation. Otherwise, use the formula. Illustrate the test statistic on the diagram of the rejection regions. Illustrate the p-value on the diagram of the rejection regions. State the decision about the null hypothesis. Interpret the decision in terms of the alternative hypothesis.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Please show work and formula, I need help with number 4, 6, and 7

A random sample of 25 frozen dinners of a certain type was selected from production during a particular period and the calorie content of each one was determined. The resulting observations are:

Calories from Frozen Dinners

255	244	239	242	265
245	259	248	225	226
251	233	266	227	246
240	257	222	237	270
230	260	268	231	238

The stated calorie content is 240 calories. At the 5% significance level, do the data suggest that the mean calorie content of the frozen dinners differs from 240 calories?

State the null and alternative hypothesis
Check the conditions. To determine if the data is approximately normal, using paper and pencil methods, construct a histogram.
If the conditions have not been satisfied, still continue with the assignment.
State the significance level. and then draw and fully label the rejection regions.
Calculate the test statistic and p-value. You may use the calculator to calculate the mean and standard deviation. Otherwise, use the formula.
Illustrate the test statistic on the diagram of the rejection regions. Illustrate the p-value on the diagram of the rejection regions.
State the decision about the null hypothesis.
Interpret the decision in terms of the alternative hypothesis.
Construct the 95% confidence interval. You may use the calculator to calculate the mean and standard deviation. Otherwise, use the formula.
Interpret the confidence interval.
Explain how the confidence interval supports the decision about the claim.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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