partial credit, 12.1.11-T A manufacturer of colored candies states that 13​% of the candies in a bag should be​ brown, 14​% ​yellow, 13​% ​red, 24​% ​blue, 20​% ​orange, and 16​% green. A student randomly selected a bag of colored candies. He counted the number of candies of each color and obtained the results shown in the table. Test whether the bag of colored candies follows the distribution stated above at the alpha equals0.05 level of significance. Determine the null and alternative hypotheses. Choose the correct answer below. A. H0​: The distribution of colors is not the same as stated by the manufacturer. H1​: The distribution of colors is the same as stated by the manufacturer. B. H0​: The distribution of colors is the same as stated by the manufacturer. H1​: The distribution of colors is not the same as stated by the manufacturer. C. None of these. Click to select your answer and then click Check Answer. 4 parts remaining Observed Distribution of Colors Colored Candies in a bag Color Brown Yellow Red Blue Orange Green Frequency 61 64 52 63 96 66 Claimed Proportion 0.13 0.14 0.13 0.24 0.20 0.16 What is the test​ statistic? chi Subscript 0 Superscript 2 equals ​(Round to three decimal places as​ needed.) What is the​ P-value of the​ test? ​P-valueequals ​(Round to three decimal places as​ needed.) Based on the​ results, do the colors follow the same distribution as stated in the​ problem? A. Do not reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. B. Do not reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. C. Reject Upper H 0. There is sufficient evidence that the distribution of colors is not the same as stated by the manufacturer. Your answer is correct.D. Reject Upper H 0. There is not sufficient evidence that the distribution of colors is not the same as stated by the manufacturer.

How do you perform Hypothesis Testing on a regression model using an ANOVA table below. This is to show the significance of the 4 independent variables.

1. Describe what qualitative forecasting models are. What are the advantages and disadvantages of this modelling?
2. “High correlation between two variables means that one is the cause and the other is the effect”. Explain this statement

Listed below are systolic blood pressure measurements​ (in mm​ Hg) obtained from the same woman. Find the regression​ equation, letting the right arm blood pressure be the predictor​ (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 100 mm Hg. Use a significance level of 0.05.

Right Arm

102

101

93

76

77

Left Arm

174

167

181

144

146

Create a research problem that would use a statistic that would explore differences(not relationships) related to something of interfere to you then identify the following: (a) population (b) sample (c) research hypothesis, (d) null hypothesis (e) the variables (f) the inferential statistics that you might use and why.

Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next twenty-five times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 20 miles per gallon and a standard deviation of 1. Find the possible sample means you are likely to get based on your sample of twenty-five observations. Consider the intervals into which 68%, 95%, and almost all of the potential sample means will fall, using the Empirical Rule. (Round all answers to the nearest thousandth.)

About 68% of possible sample means will be in the range between ___ and ____ .

About 95% of possible sample means will be in the range between ____ and ____ .

About 99.7% of possible sample means will be in the range between ____ and ____.

The weight of football players in the NFL is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.

A) What is the probability that a randomly selected football player will weigh more than 243.75 pounds?

B) What is the probability that a football player will weigh less than 260 pounds?

C) What percentage of players will weigh between 150 to 250 pounds?

D) 95% of player weights are less than X pounds. Therefore X is?

A random sample of 81 observations is drawn from a population with a mean of 104 and a variance of 156.25.

a) State the distribution of the sample mean, ?̅. (Show any conditions that you have checked.)

b) Calculate the probability that the sample mean is at most 102.5.

c) Calculate the probability that the sample mean is between 103.5 and 105.8.

7.A random sample of 49 observations is drawn from a population with a normal distribution. If the sample mean is 265 and the sample standard deviation is 57, find the 95% confidence interval for the population mean.

8. A random sample of 49 observations is drawn from a population with a normal distribution with a standard deviation of 57. If the sample mean is 265, find the 95% confidence interval for the population mean. Compare this confidence interval with the one found in question 7. Finally, find the 99% confidence interval for the population mean. How does this compare to the 95% confidence interval?

The wait time at the Goleta Post Office is uniformly distributed between 1 and 16 minutes.

a) Define the random variable of interest, X.

b) State the distribution of X.

c) What is the average wait time?

d) Calculate the probability that the wait time is more than 17 minutes.

e) Calculate the probability that the wait time is at least 10 minutes.

f) Calculate the probability that the wait time is between 2 and 11 minutes

A researcher is interested in the mean amount of time it takes people to complete a personality questionnaire. He selects 40 people at random and calculates the mean amount of time to be 20.4 min with a variance of 17.64 min2 .

a) Define the parameter of interest.

b) Define the random variable of interest.

c) Name the distribution required to calculate confidence intervals. (Check the relevant criteria.)

d) Construct a 98% confidence interval for the true mean amount of time.

e) Interpret your confidence interval.

A university has 15,000 students. We have drawn a simple random sample size of 400 from the population and recorded how much money each student spent on cellular telephone service during November 2003. For this sample, the sample mean is $36, and sample standard deviation is $20. At a 99% level of confidence, test the null hypothesis that these 15,000 students, combined, did not spend more than $500,000 on cellular telephone service during November 2003.

A computer manufacturer believes that the proportion of hardware malfunctions is different in humid climates than in dry climates. To test this claim, the manufacturer takes a random sample of 400 machines sold in Florida (humid) and 400 machines sold in Arizona (dry). The manufacturer finds that 44 of the machines in Florida and 24 of the machines in Arizona had hardware malfunctions.

a. Specify the competing hypotheses to test the manufacturer's claim.

b. Calculate the value of the relevant test statistic.

c. Compute the p-value. Does the evidence support the computer manufacturer's claim at the 10% significance level?

Name and discuss four probability distributions , highlight their characteristics , how they are similar to one another , and how they differ from one another , and hoe they differ from one another?

A worker for measurement Canada suspects a gas station chain has calibrated its pumps to deliver less fuel than advertised. 15 pumps are sampled by dispensing gas into a graduated container, until the metered amount of gasis exactly 40 L. From your sample, you calculate the mean amount dispensed is x̅ = 39.7 L, with s = 0.6 L. At the α = 0.05 level of signifciance, test the hypothesis that the station pumps deliver less than 40 L. Assume that all conditions for testing hypothesis have been met.

a) Clearly defining any symbols, state the null and alternative hypothesis in symbolic form?

b) Calculate the value of the test statistic for testing above hypothesis

c) Calculate only one of the rejection region or the p-value for the above test.

d) State the conclusion and interpretation for the test

e) Describe the consequences of a type I error in this scenario.