Use a 0.05 significance level to test the claim that peanut candies have weights that vary more than plain candies. The standard deviation for the weights of plain candies is 0.325. A sample of 81 peanut candies has weights with a standard deviation of 0.38. Assume the population is normally distributed. (a) Write the claim mathematically and identify Upper H 0H0 and Upper H Subscript aHa. A. Upper H 0 : sigma equals 0.325H0: σ=0.325; Upper H Subscript a Baseline : sigma not equals 0.325Ha: σ≠0.325 (Claim) B. Upper H 0 : sigma less than or equals 0.325H0: σ≤0.325; Upper H Subscript a Baseline : sigma greater than 0.325Ha: σ>0.325 (Claim) C. Upper H 0 : sigma greater than or equals 0.325H0: σ≥0.325 (Claim); Upper H Subscript a Baseline : sigma less than 0.325Ha: σ<0.325 (b) Find the critical value(s). Blank (Use a comma to separate answers as needed. Round to three decimal places as needed.) (c) Use the chiχsquared2-test to find the standardized test statistic. Blank (Round to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Fail to reject Reject (e) Interpret the decision in the context of the original claim. Does it appear that peanut candies have weights that vary more than those of plain candies? A. Since the null hypothesis isis rejected, the weights appearappear to vary more for peanut candies. B. Since the null hypothesis isis rejected, the weights do not appeardo not appear to vary more for peanut candies. C. Since the null hypothesis is notis not rejected, the weights do not appeardo not appear to vary more for peanut candies. D. Since the null hypothesis is notis not rejected, the weights appearappear to vary more for peanut candies.

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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Concept explainers

Question

Use a

0.05

significance level to test the claim that peanut candies have weights that vary more than plain candies. The standard deviation for the weights of plain candies is

0.325.

A sample of

peanut candies has weights with a standard deviation of

0.38.

Assume the population is normally distributed.

(a) Write the claim mathematically and identify

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0 : sigma equals 0.325H0: σ=0.325;

Upper H Subscript a Baseline : sigma not equals 0.325Ha: σ≠0.325

(Claim)

Upper H 0 : sigma less than or equals 0.325H0: σ≤0.325;

Upper H Subscript a Baseline : sigma greater than 0.325Ha: σ>0.325

(Claim)

Upper H 0 : sigma greater than or equals 0.325H0: σ≥0.325

(Claim); Upper H Subscript a Baseline : sigma less than 0.325Ha: σ<0.325

(b) Find the critical value(s).

Blank

(Use a comma to separate answers as needed. Round to three decimal places as needed.)

chiχsquared2-test

to find the standardized test statistic.

Blank

(Round to three decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Fail to reject

Reject

(e) Interpret the decision in the context of the original claim.

Does it appear that peanut candies have weights that vary more than those of plain candies?

Since the null hypothesis

isis

rejected, the weights

appearappear

to vary more for peanut candies.

Since the null hypothesis

isis

rejected, the weights

do not appeardo not appear

to vary more for peanut candies.

Since the null hypothesis

is notis not

rejected, the weights

do not appeardo not appear

to vary more for peanut candies.

Since the null hypothesis

is notis not

rejected, the weights

appearappear

to vary more for peanut candies.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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