The production line at the Heinz ketchup factory is calibrated to fill bottles of ketchup with no more than 24 ounces of ketchup in each bottle. We certainly do not want ketchup to spill onto the assembly line equipment; that would create a mess.

In order to test how well our machinery is working, a sample of 70 bottles are randomly selected from a days production of filled ketchup bottles and the contents of each bottle are measured. The sample reveled a mean of 24.1 ounces per bottle, with a sample standard deviation of 0.3 ounces.

Use an α = .05.

A. Provide the appropriate hypothesis test criteria:

B. Using the data from the sample, answer the five fill-in-the-blank questions, and make the correct hypothesis test conclusion.

Based on these results, we should:

• Reject Ho

• Accept Ho

C. Should Heinz shut down the production line?

This question will be sent to your instructor for grading.

According to a newspaper article, teens watch on average 315 minutes of television a week. A concerned parent collected a random sample of 12 individual teens to test the claim. The sample average for the number of minutes was 337. The sample standard deviation was 55 minutes. With alpha = 0.1, is there enough evidence to reject the article's claim?

a) Is this a test that uses, z-scores, t-scores, or chi-squared values?

b) Does this problem involve proportions?

c) What is(are) the critical value(s) for the problem?

d) What is the test value and which formula did you use? The formulas are numbered.

e) Should the researcher reject the claim?

The present study shows data for direct flights from Orlando to Miami for one airline. The airline claims that the flying time (time in the air) of direct flights from Orlando to Miami takes 45 minutes. The company would like to test the claim and collects a random sample of 90 flights. We will find the average and standard deviation for the flights’ times for the random sample of flights. We will use Excel functions to find the critical value(s) that define(s) the rejection region. We will use formulas to find the test statistic, compare it with our critical value(s), and decide if we should reject or not reject the null hypothesis. We will use different alpha levels to test the hypothesis. We will find the observed level of significance and use it to make conclusions about the claim. We will identify possible errors made and their types. Assume that the distribution of the flight times is normal and the sample is randomly selected.

1) find the Standard Deviation of the flight time for the sample flights

2) find the sample size of the sample of flights

3) to test the null hypothesis for the mean flight time, what is the appropriate probably table to use?

4) identify the degrees of freedom needed to find the critical values?

5) the company would like to test the claim (null hypothesis) that the flight takes 45 minutes against the alternative that it does not. is this a two sided test?

6) find the value of the test statistic

7) find a one-sided critical value from the appropriate probability table to test the claim at alpha = 0.05

8) What is/are the sign(s) of the critical value(s) for the test of the hypothesis at alpha=0.05?

9) By assessing the answers above, do you reject the null hypothesis? why?

Show formula if possible. Thank you

Between 20 and 25 violent acts are portrayed per hour on children’s TV. A study by Johnson et al (2002) looked for links between TV viewing and aggression by following the TV viewing habits of children 1-10 years old. Of these, 88 watched < 1 hr TV per day, 386 watched 1-3 hrs and 233 watched > 3 hrs. Eight years later, researchers looked to see if any of the children had records of aggressive assaults on other people. The numbers of children with aggressive assaults were 5, 87 and 67 for each TV category, respectively. The remaining children were not aggressive.

Question 1: Create a contingency table of the results from the study. Carry out an appropriate statistical test to determine whether TV viewing is associated with future violence. What is the conclusion from your test?

Question 2: Do the results of the study prove that TV watching behavior causes increased aggression in children? Why?

The herbal supplement biloba ginko is advertised as producing an increase in physical strength and stamina. To test this claim, a sample of n = 27 adults is obtained and each person is instructed to take the regular dose of the herb for 45 days. At the end of the 45-day period, each person is tested on a standard treadmill task for which the average score for the population is µ = 18. The individuals in the sample produce a mean score of M = 21.2 with SS = 1460.

1.) Are these data sufficient to conclude that the herb has a statistically significant effect on stamina using a two-tailed test with alpha = .05? Be specific here (in other words, reject or retain the null and why and then interpret what that means). Make sure to show all four (or five) steps.

2.) What decision would be made if the researcher used a one-tail test with alpha = .05 and why? Be specific.

A random sample of 853 births included 430 boys. Use a 0.10 significance level to test the claim that 51.2 ​% of newborn babies are boys. Do the results support the belief that 51.2 ​% of newborn babies are​ boys?

Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0 ​: pequals 0.512Upper H 1 ​: pnot equals 0.512 B. Upper H 0 ​: pequals 0.512Upper H 1 ​: pgreater than 0.512 C. Upper H 0 ​: pequals 0.512Upper H 1 ​: pless than 0.512 D. Upper H 0 ​: pnot equals 0.512Upper H 1 ​: pequals 0.512

Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is negative .-.46 ​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test. The​ P-value for this hypothesis test is _____

Please show step by step to find the P-value, I am getting really confused on how to do it.I need someone to explain how i used the z-score table method and the calculator method. Specifically please tell me what do I type in the calculator,

5.    Thank you!!

A researcher is interested in determining whether the illumination level in a room affects how quickly clients can be put into a trance. The time (in seconds) it took for five clients to go into a trance when it was done in a room that was lit with low light was measured, as was the time it took for the same clients to go into a trance in a brightly lit room. The theory being tested does not predict which light condition will lead to going into a trance more quickly. The data are given below:

SS_D=?

est. σ²_D=?

est. σ_D=?

est. σ_MD=?

Estimate the effect size of the independent variable?

Consider an engine parts supplier and suppose they determined that the variance of all cylindrical engine parts diameters produced by the current machine is .007. To reduce this variance, a new machine is designed. A random sample from the new machine is taken of 25 parts, which have a variance of .0046. At the 1% significance level, can we conclude that the new machine produces a smaller diameter variance? Please show all work hand written.

Your company's new portable phone/music player/PDA/bottle washer, the RunMan, will compete against the established market leader, the iNod, in a saturated market. (Thus, for each device you sell, one fewer iNod is sold.) You are planning to launch the RunMan with a traveling road show, concentrating on two cities, New York and Boston. The makers of the iNod will do the same to try to maintain their sales. If, on a given day, you both go to New York, you will lose 900 units in sales to the iNod. If you both go to Boston, you will lose 650 units in sales. On the other hand, if you go to New York and your competitor to Boston, you will gain 1,600 units in sales from them. If you go to Boston and they to New York, you will gain 600 units in sales. What fraction of time should you spend in New York and what fraction in Boston?

You should spend  of your time in New York and  in Boston.

How do you expect your sales to be affected?

1. A particular event has a probability of occurrence of p=0.65. Given 12 independent trials, draw the probability distribution and calculate the expected value.
2. A particular event has a probability of occurrence of p=0.65. If each outcome is independent of the last, draw the probability distribution associated with the event not occurring a given number of consecutive times and calculate the expected value.
3. Given the following scenario, determine which distribution (binomial, geometric, hypergeometric) is the most appropriate to model it? Rank the distributions from most appropriate to least appropriate. Explain the reason(s). "1600 students attend BOSS. It is determined that 70% of all BOSS students wear glasses. If groups of 50 students were selected at random, how many of them would be wearing glasses?"

A researcher designed a study to find out the effectiveness of two teaching methods: lecture-style vs. discussion-style. He compares the test scores of the students taught with these two different methods. The scores on the test range from 0 to 41 with higher scores indicating better performance. The test results are provided in the table below:

                                    Group       Methods                  n              M             SS
                                       1             lecture-style          15             24            336
                                       2             discussion-style    15             28             392

1. Do students taught with the discussion style perform better than those taught with the lecture style? Use the .05 significance level for the one-tailed test. Show the four steps of hypothesis testing, and describe the hypotheses and conclusion in words as well as notations

2. Compute (show calculation steps) and interpret r²

1. In an earlier poll, it was determined that 55% of the population support the prime minister. Today, 100 people were polled and 50% of respondents approve. If these polls are conducted weekly, can one claim that the prime minister's popularity has decreased? Explain your thinking with the help of appropriate calculations.
2. Research on a new medication shows it is 85% effective in relieving allergy symptoms. In other words, 85 in 100 people would report feeling better a day after taking the drug. How many users of the medication would have to be surveyed before being 99.9% sure that at least someone felt relief?

What is the area to the right of three in the graph below?

The number of chocolate chips in an​ 18-ounce bag of chocolate chip cookies is approximately normally distributed with mean 1252 and standard deviation 129 chips. ​

(a) What is the probability that a randomly selected bag contains between 1000 and 1400 chocolate​ chips? ​

(b) What is the probability that a randomly selected bag contains fewer than 1100 chocolate​ chips? ​

(c) What proportion of bags contains more than 1225 chocolate​ chips?

​(d) What is the percentile rank of a bag that contains 1475 chocolate​ chips?