P(H)=2/3,P(T)=1/3, a coin  is thrown 3times,X is a random variable that shows the number of getting head

a) find the distribution of X

b)find the expected value of X

c) find the variannce of X

d)find the standard deviation of X

19. An aircraft manufacturer requires bolts that are part of the landing gear assembly to have a mean diameter of 1.1 inches with a variance of no more than 0.04 inches2. The bolts are purchased from an outside supplier. A random sample of 30 bolts from a recently received shipment yielded a variance of 0.054 inches2. Should the shipment be returned? Perform the appropriate test of hypothesis using alpha = 0.05. (15 points) T

est Statistic = ______________

Reject Region: Reject H0 x^2 if > ______________

Conclusion: ______________

Conclusion about shipment: ______________

A hotel chain wanted to learn about the level of experience of its general managers. A random sample of 14 general managers was taken, and these managers had a mean of 11.72 years of experience. Suppose that the standard deviation of years of experience for all general managers in the chain is known to be 3.2 years. What is the lower limit of a 95% confidence interval for the mean experience of all general managers in this hotel chain?

Box X contains 3 red, 2 white marbles; box Y contqains red, white marbles A box os selected at random; a marble is drawn and put into the other box; then a marble is drawn from the second box Find the probability that both marbles drawn are of the same color

Blair & Rosen, Inc. (B&R) is a brokerage firm that specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client who contacted B&R this past week has a maximum of $50,000 to invest. B&R's investment advisor decides to recommend a portfolio consisting of two investment funds: an Internet fund and a Blue Chip fund. The Internet fund has a projected annual return of 12%, while the Blue Chip fund has a projected annual return of 9%. The investment advisor requires that at most $35,000 of the client's funds should be invested in the Internet fund. B&R services include a risk rating for each investment alternative. The Internet fund, which is the more risky of the two investment alternatives, has a risk rating of 6 per thousand dollars invested. The Blue Chip fund has a risk rating of 4 per thousand dollars invested. For example, if $10,000 is invested in each of the two investment funds, B&R's risk rating for the portfolio would be 6(10) + 4(10) = 100. Finally, B&R developed a questionnaire to measure each client's risk tolerance. Based on the responses, each client is classified as a conservative, moderate, or aggressive investor. Suppose that the questionnaire results classified the current client as a moderate investor. B&R recommends that a client who is a moderate investor limit his or her portfolio to a maximum risk rating of 240.

Hypothesis Testing. Follow the description of the assignment below.

Think of a problem of your interest, set up H0 and Ha and conduct the hypothesis test.

Describe the research problem. Determine the level of significance – use the levels: α=0.1 ,α=0.05 or α=0.01.

Identify the target population and the population parameter of interest (μ or p; μ_1- μ_2 or p_1-p_2). Set up H0 and Ha.

Provide sample evidence: (1) Data source: a) primary sources i.e. survey, experiment, observation or b) secondary sources i.e. database/registry, census, internet portals etc.; (2) Sample properties: random, large or small sample; and (3) Sample data: sample size, sample mean(s) or sample proportion(s).

Define critical test statistic values (z or t-value). Calculate sample test-statistics and observed significance level (p-value).

Evaluate the sample evidence: (1) compare the critical values for rejection with sample statistics values and (2) compare observed significance level (p-value) with significance level (α).

Provide conclusion (whether you reject or do not reject H0) and interpret the results.

The assignments are subject to teacher assessment. Good projects... • ... are based on an original and meaningful research problem, and on representative and interesting sample evidence; • ...present a correctly conducted hypothesis testing procedure with a valid conclusion and well interpreted results; • ...are clear, and have a nice presentation (include images if relevant).

Given two independent random samples with the following results:

n1=8 x‾1=109 s1=35 n2=12 x‾2=145 s2=20

Use this data to find the 98% confidence interval for the true difference between the population means. Assume that the population variances are not equal and that the two populations are normally distributed.

Copy Data

Refer to the accompanying data set of mean drive-through service times at dinner in seconds at two fast food restaurants. Construct a 99% confidence interval estimate of the mean drive-through service time for Restaurant X at dinner; then do the same for Restaurant Y. Compare results.
Construct a 99% confidence interval of the mean drive-through service times at dinner for Restaurant X.
Restaurant X   Restaurant Y
85   104
117   130
119   149
151   119
262   174
183   130
125   114
148   127
157   129
216   130
336   129
308   141
175   227
111   209
151   294
145   123
92   93
233   138
235   240
181   146
155   140
196   206
164   147
120   146
60   134
203   146
181   157
114   131
136   167
174   130
184   238
194   238
227   252
194   234
350   234
307   165
210   88
198   104
183   51
185   168
103   77
147   148
176   144
161   101
172   122
155   144
168   126
119   184
140   154
312   126

Assume that :

The first column is the weight gain of the people in the quarantine in the first week in kilogram (WG) .

   The second column is describing the gender whether it was male or female (G) .

Q: Is there any statistical evidence that the gaining weight for the females is higher than the gaining weight for the males ? Show your work .  

Use the sample data and confidence level given below to complete parts​ (a) through​ (d). In a study of cell phone use and brain hemispheric​ dominance, an Internet survey was​ e-mailed to 2562 subjects randomly selected from an online group involved with ears. 1057 surveys were returned. Construct a 90​% confidence interval for the proportion of returned surveys. LOADING... Click the icon to view a table of z scores. ​a) Find the best point estimate of the population proportion p. nothing ​(Round to three decimal places as​ needed.) ​b) Identify the value of the margin of error E. Equals nothing ​(Round to three decimal places as​ needed.) ​c) Construct the confidence interval. nothing less than p less than nothing ​(Round to three decimal places as​ needed.) ​d) Write a statement that correctly interprets the confidence interval. Choose the correct answer below. A. One has 90​% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion. B. 90​% of sample proportions will fall between the lower bound and the upper bound. C. One has 90​% confidence that the sample proportion is equal to the population proportion. D. There is a 90​% chance that the true value of the population proportion will fall between the lower bound and the upper bound.

The mean of the binomial distribution 10∁x ( 2/3 )^x ( 1/3 ) ^ 10 -x is given by

The following dataset contains a random sample of lifetime of 120 BMW Xenon headlight bulbs. The manufacturer of these bulbs wants to know whether it can claim that the bulbs last more than 1000 hours. Use a=0.01

a)Formulate the hypotheses.

b)What is the value of the test statistic?

c)What are the critical values of the test?

d)Find the p-value of the test.

e)What is your conclusion? Explain it in the context of the problem.

Let X be from a normal distribution with mean u and varince 4. We would like to test the null hypothesis H0: u=10 against the alternative hypothesis H1: u>10. Let the rejection region be defined by C={(x1,x2,...,x9): X.bar>=11.5}, where X.bar is the sample mean of a random sample of size 9 from this distribution.

(a) what's the significance level of this test?

(b) Define the power function for this test.

(c) what are the power when u=11, 11.5 and 12?

Each of three supermarket chains in the Denver area claims to have the lowest overall prices. As part of an investigative study on supermarket advertising, a local television station conducted a study by randomly selecting nine grocery items. Then, on the same day, an intern was sent to each of the three stores to purchase the nine items. From the receipts, the following data were recorded. At the 0.025 significance level, is there a difference in the mean price for the nine items between the three supermarkets?

  Click here for the Excel Data File

1. State the null hypothesis and the alternate hypothesis.

For Treatment (Stores): Null hypothesis

1. H₀: μ₁ ≠ μ₂ ≠ μ₃

2. H₀: μ₁ = μ₂ = μ₃

A) a

B ) b

2. Alternate hypothesis

A) H₁: There is no difference in the store means

B )H₁: There is a difference in the store means.

3. For blocks (Items):

1. H₀: μ₁ = μ₂ = ... μ₉

2. H₀: μ₁ ≠ μ₂ ≠ ... μ₉

A) a

B) b

4. Alternate hypothesis

A) H₁: There is no difference in the item means.

B) H₁: There is a difference in the item means.

5. What is the decision rule for both? (Round your answers to 2 decimal places.)

6. Complete an ANOVA table. (Round your SS, MS to 3 decimal places, and F to 2 decimal places.)

7. What is your decision regarding the null hypothesis? The decision for the F value (Stores) at 0.025 significance is:

A )Reject H₀

B) Do not reject H₀

8. The decision for the F value (Items) at 0.025 significance is: A)Reject H₀ B) Do not reject H₀

9. Is there a difference in the item means and in the store means?