Suppose that you are the manager of a casino and you collect data on one of your roulette tables. You find that among the last 10,000 bets, there were only 350 bets for which a red or black number did not win. On average, you expect the proportion of winning bets for black or red to equal p=18/19.

a) Compute a 95% confidence interval for the proportion of winning black or red bets.

b) Conduct a two-sided hypothesis test (α=0.05)for HO: p=18/19. State the relevant p-value and your decision whether to reject or not reject HO.

c) Compare your results in part (a) and (b). Are they consistent?

PTC is a substance that has a strong bitter taste for some people and is tasteless for others. The ability to taste PTC is inherited and depends on a single gene that codes for a taste receptor on the tongue. Interestingly, although the PTC molecule is not found in nature, the ability to taste it correlates strongly with the ability to taste other naturally occurring bitter substances, many of which are toxins. About 75%75% of Italians can taste PTC. You want to estimate the proportion of Americans with at least one Italian grandparent who can taste PTC.

(a) Starting with the 75%75% estimate for Italians, how large a sample must you collect in order to estimate the proportion of PTC tasters within ±0.1±0.1 with 90%90% confidence? (Enter your answer as a whole number.)

(b) Estimate the sample size required if you made no assumptions about the value of the proportion who could taste PTC. (Enter your answer as a whole number.)

You want to test your hypothesis below:

There is a difference in mean test scores between two classes: Class 1 vs. Class 2

            Provide your answers in the template below the data set.

Two sample Independent t-test

You want to test your hypothesis below:

There is a difference in developing skills by practice methods: Distributed practice vs. Massed practice.

            Provide your answers in the template below the data set.

Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per week?”

10) Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox.

11) Use the Excel function =CORREL to compute the correlation. If answers for #1 and 2 do not agree, there is an error.

12) The strength of the correlation motivates further examination.

a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis.

b) Add to your chart: the chart name, vertical axis label, and horizontal axis label.

c) Complete the chart by adding Trendline and checking boxes

13) Read directly from the chart:

a) Intercept =

b) Slope =

c) R2 =

Perform Data > Data Analysis > Regression.

14) Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the total standard error in orange

SUMMARY OUTPUT

For the record, this is a homework question, not a test question. Why is the t-distribution sometimes used when calculating a confidence interval? b) (2 points) In general, is the =t.inv value larger or smaller than the =norm.inv value for a given level of confidence. c) (4 points) How do t and z compare as the sample size increases? Be sure to include a graph in your answer. Your graph should include t with a small sample size, t with a large sample size, and z.

Suppose a group of 700 smokers (who all wanted to give up smoking) were randomly assigned to receive an antidepressant drug or a placebo for six weeks. Of the 164 patients who received the antidepressant drug, 41 were not smoking one year later. Of the 536 patients who received the placebo, 107 were not smoking one year later. Given the null hypothesis H0:(pdrug−pplacebo)=0 and the alternative hypothesis Ha:(pdrug−pplacebo)≠0, conduct a test to see if taking an antidepressant drug can help smokers stop smoking. Use α=0.01

,

(a) The test statistic is

(b) The P-value is

(c) The final conclusion is

A. There is not sufficient evidence to determine whether the antidepressant drug had an effect on changing smoking habits after one year.
B. There seems to be evidence that the patients taking the antidepressant drug have a different success rate of not smoking after one year than the placebo group.

An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.73 inch. The lower and upper specification limits under which the ball bearing can operate are 0.715 inch​ (lower) and 0.745 inch​ (upper). Past experience has indicated that the actual diameter of the ball bearings is approximately normally​ distributed, with a mean of 0.734 inch and a standard deviation of 0.006 inch. Suppose a random sample of 22 ball bearings are selected. Complete parts​ (a) through​ (e). What is the probability that the sample mean is between the target and the population mean of 0.734​? What is the probability that the sample mean is between the lower specification limit and the​ target? What is the probability that the sample mean is greater than the upper specification​ limit? What is the probability that the sample mean is less than the lower specification​ limit? The probability is 92​% that the sample mean diameter will be greater than what​ value?

Thank you in advance, i'm not so good with this subject so could you include the steps you did please

1. The gross weekly sales at a certain super market are a Gaussian random with mean $2200 and standard deviation $230. Assume that the sales from week to week are independent. (a) Find the probability that the gross sales over the next two weeks exceed $5000. (b) Find the probability that the gross weekly sales exceed $2000 in at least 2 of the next 3 weeks.

2. Let ?1,?2,?3 and ?4 be pairwise uncorrelated random variables each with zero mean and unit variance. Compute that correlation coefficient between

(a) ?1 + ?2 and ?2 + ?3. (b) ?1 + ?2 and ?3 + 4.

3. Let the random variables ? be the sum of independent Poisson distributed random variables, i.e., ? = ∑ ? (top) ?=1(bottom) ?? , where ?? is Poisson distributed with mean ?? .

(a) Find the moment generating function of ?? . (b) Derive the moment generating function of ?. (c) Hence, find the probability mass function of ?.

4. Let ? and ? be independent and identically distributed random variables with mean ? and variance ?^2. Find the following:

(a) ?[(? + 7) ^2 ]

(b) Var(8? + 9)

(c) ?[(? − ?) ^2 ]

(d) Cov{(? + ?), (? − ?)}

5. The moment generating function of the random variable X is given by ??(?) = exp{7(?^(?)) − 7} and that of ? by ?? (?) = ( (8/9) (?^(?)) + (6/9))^10 . Assuming that ? and ? are independent, find

(a) ?{? + ? = 7}.

(b) ?{?? = 0}.

(c) ?(??).

Hypothesis test of one mean

1. A random sample of eight students participated in a psychological test of depth perception. Two markers, one labeled A and the other B, were arranged at a fixed distance apart at the far end of the laboratory. One by one the students were asked to judge the distance between the two markers at the other end of the room. The sample data (in feet) were as follows:

2.2, 2.3, 2.7, 2.4, 1.9, 2.4, 2.5, 2.6

At the alpha =0.05 level of significance, test if the mean distance is more than 2 feet

1. State the null and alternative hypothesis.
2. Give the p-value
3. Give a conclusion for the hypothesis test.
4. Find a 95% Confidence Interval.
5. Write a conclusion for the confidence interval

Hypothesis test of two means

2. A random sample of non-English majors at a selected college was used in a study to see if the student retained more from reading a 19^th century level novel or by watching it in DVD form. Each student was assigned one novel to read and a different one to watch, and then they were given a hundred point quiz on each novel. The test results are shown:

DVD          90 82 85 95 70 75 85

BOOK       95 85 95 75 85 95 84

Alpha = 0.05, can it be concluded that the DVD scores are less than the BOOK?

1. State the null and alternative hypothesis.
2. Give the p-value.
3. Give a conclusion for the hypothesis test.

Hypothesis test of one proportion

3. The national average for the percentage of high school graduates taking the SAT is 49%. A random sample of 300 high school graduating seniors were polled across a particular tri state area, and it was found that 195 had taken the SAT.

At alpha = 0.05 level of significance, does the proportion of high school graduates who take the SAT in this area agree with the national average?

1. State the null and alternative hypothesis.
2. Give the p-value.
3. Give a conclusion for the hypothesis test.
4. Find a 95% Confidence Interval.
5. Write a conclusion for the confidence interval.

Hypothesis test of two proportions

4. The drug Prevnar is a vaccine meant to prevent certain types of bacterial meningitis. It is typically administered to infants starting around two months old. In a randomized doubled-blind clinical trials of Prevnar, infants were randomly divided into two groups. Group 1 received Prevnar while Group 2 received a control vaccine. After the second dose, 137 of 452 subjects in group 1 effect experienced drowsiness as a side effect. After the second dose, 31 of 99 subjects in Group 2 experienced drowsiness as a side effect. Does the evidence suggest that there is a different proportion between the groups at alpha =0.05 level of significance?

(a) State the null and alternative hypothesis

(b) Give the p-value

(c) Give a conclusion for the hypothesis test.

Write the null and alternative hypotheses for each of the following examples. Determine if each is a case of a two-tailed, a left-tailed, or a right-tailed test. (a) To test if the mean number of hours spent working per week by college students who hold jobs is different from 20 hours (b) To test whether or not a bank’s ATM is out of service for an average of more than 10 hours per month (c) To test if the mean length of experience of airport security guards is different from 3 years (d) To test if the mean credit card debt of college seniors is less than $1000 (e) To test if the mean time a customer has to wait on the phone to speak to a representative of a mailorder company about unsatisfactory service is more than 12 minutes

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to determine of the mean number of unoccupied seats on all its flights is greater than 10. To accomplish this, the records of 60 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.4 seats and the sample standard deviation is 3.4 seats. Test the claim that mean number of unoccupied seats on all its flights is greater than 10 at the 5% significance level.

A television CEO believes viewership of the evening news does not depend on age. She collects a random sample of 2000 television viewers across four different age groups and asks whether or not they watch the evening news. The results are as follows:

Watch              | 18 years old             19 to 35                36 to 54            55 years old

Evening News | or less                       years old              years old             or more

_____________________________________________________________________

Yes                  |           70                        96                          112                  146

                        |

No                   |           430                      404                         388                  354

                        |

_____________________________________________________________________

Test to see whether watching the evening news and age grouping are independent at the 0.05 level using the Chi-Square test. Conduct this test by hand and using the Chi-Square table.

For a standardized normal​ distribution, determine a​ value, say z0​, such that the following probabilities are satisfied.

a. ​P(0less thanzless thanz0​)equals0.4641

b. ​P(minusz0less than or equalszless than​0)equals0.34

c. ​P(minusz0less than or equalszless than or equalsz0​)equals0.91

d. ​P(zgreater thanz0​)equals0.035 e. ​P(zless than or equalsz0​)equals0.02