For the following data, approximate the sample mean, sample variance and sample standard deviation weekly grocery bill.

Bill (in dollars) Frequency

135-139 11

140-144 20

145-149 19

150-154 7

155-159 5

find a research article that uses hypotheses. Identify the hypotheses as null or alternative. Some articles will contain more than one hypothesis. Then, look at the discussion part of the article and see if the p-values were significant and discuss how the article presented the acceptance or rejection of the hypothesis. Include the pdf of the article with your first discussion posting.

4. To determine the effectiveness of a proposed public relations campaign, the senior vice president for customer relations for an automobile manufacturer asked seven consumers how much they liked the company (on a scale from 0 [do not like] to 50 [like very much]) before and after viewing the primary television advertisement of the campaign. Use the following data to test whether the consumers’ ratings of the company increased, on average, after viewing the television advertisement:

a. State the null and alternative hypotheses associated with the test.
b. If α = 0.05, what is the critical value of the associated test statistic?
c. What is the calculated value of the associated test statistic?
d. State your decision about the null hypothesis by comparing the critical and calculated values of the test statistic (Parts b and c).
e. Comment on the effectiveness of the primary television advertisement of the campaign.

A mixture of pulverized fuel ash and Portland cement used for grouting should have a compressive strength of more than 1300 KN/m². The mixture will not be used unless experimental evidence indicates conclusively that the strength specification has been met, that is, the true mean compressive strength is more than 1300. Suppose compressive strength for specimens of this mixture is normally distributed with standard deviation of 60. A sample of 10 randomly chosen specimens has a sample mean compressive strength of 1331.26.

a) What are the appropriate null and alternative hypotheses?

b) Carry out the test from part a) at 5% level of significance stating clearly the conclusion in the context of the question.

c) What is the probability of making a Type I error in part b) and describe it in the context of the question?

d) Compute an appropriate one-sided 95% confidence bound for the true mean compressive strength and explain why you chose this bound in the context of the question.

THE ANSWERS FOR THIS PROBLEM ARE AS FOLLOWS:

a) Null: ?=1300, Alternative: ?>1300?

b) z=1.6475, z0.05 = 1.645, z>z0.05 at 5% and mean>1300, so we reject the null.

c) ? = 0.05, Reject null when true. Conclude ?>1300 when it is not.

d) lower: 1300.04 and 1300 is below. ?>1300.

Please explain the steps for how to solve this problem. Thank you!

The following table reports the fasting glucose levels of a sample of potential participants in a research study investigating the efficacy of a new insulin-type drug.

A) Calculate the mean, median, mode, and standard deviation for the group.
B) Are there any potential outliers that may be affecting the statistics calculated in part A?

A medical researcher says that less than 24​%of adults in a certain country are smokers. In a random sample of 250 adults from that​ country,18.8​% say that they are smokers. At

alphaαequals=0.05, is there enough evidence to support the​ researcher's claim? Complete parts​ (a) through​ (e) below.​(a) Identify the claim and stateUpperH0and Upper H Subscript aHa.

What is the​ claim?

A.Less than 24​%of all adults are smokers.

B.Exactly 18.8​%of all adults are smokers.

C.Exactly 18.8​% of adults in the country are smokers.

D.Less than 24​%of adults in the country are smokers.Identify

Upper H0 and Upper H Subscript aHa.Upper H0​:

less than<greater than or equals≥greater than>less than or equals≤nothing

Upper H Subscript aHa​:

greater than>less than or equals≤not equals≠less than<greater than or equals≥nothing

​(Type integers or​ decimals.)

​(b) Find the critical​ value(s) and identify the rejection​ region(s).

The critical​ value(s) is/arez 0z0equals=nothing.

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

What​ is/are the rejection​ region(s)? Select the correct choice below and fill in the answer​ box(es) to complete your choice.

​(Round to three decimal places as​ needed.)A.zless than<nothingandzgreater than>nothing

B.zless than<nothing

C.zgreater than>nothing

​(c) Find the standardized test statistic z.zequals=nothing (Round to two decimal places as​ needed.)

​(d) Decide whether to reject or fail to reject the null hypothesis and​ (e) interpret the decision in the context of the original claim.

Reject or Fail to reject Upper H 0H0.

There is not or is enough evidence at the 55​%level of significance to support or reject the​ researcher's claim that less than 24% or exactly 18.8% of all adults or adults in the country are smokers.

1/12/2018 Section 9.1 Homework-Rachel Yehnert

2. Since an instant replay system for tennis was introduced at a major tournament, men challenged 1391 referee calls, with the result that 423 of the calls were overturned. Women challenged 765 referee calls, and 227 of the calls were overturned. Use a 0.01 significance level to test the claim that men and women have equal success in challenging calls. Complete parts (a) through (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of male tennis players who challenged referee calls and the second sample to be the sample of female tennis players who challenged referee calls. What are the null and alternative hypotheses for the hypothesis test?

A. H0:p1≥p2 H1: p1 ≠p2 D. H0:p1=p2 H1: p1 >p2

Identify the test statistic.

B. H0:p1=p2 H1: p1 <p2 E. H0:p1≤p2 H1: p1 ≠p2

C. H0 : p1 = p2 H1: p1 ≠p2 F. H0:p1≠p2 H1: p1 =p2

z= 0.36
(Round to two decimal places as needed.)

Identify the P­value.

P­value = 0.721
(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

The P­value is greater than the significance level of = 0.01, so
is not sufficient evidence to warrant rejection of the claim that women and men have equal success in challenging calls.

b. Test the claim by constructing an appropriate confidence interval.
The 99% confidence interval is − 0.046 < p1 − p2 < 0.060 .

(Round to three decimal places as needed.)
What is the conclusion based on the confidence interval?

Because the confidence interval limits include 0, there does not appear to be a significant difference between the

two proportions. There is not sufficient evidence to warrant rejection of the claim that men and women have equal success in challenging calls.

c. Based on the results, does it appear that men and women have equal success in challenging calls?

It does not appear that men and women have equal success in challenging calls. Women have more

success.

It appears that men and women have equal success in challenging calls.

It does not appear that men and women have equal success in challenging calls. Men have more success.

The results are inconclusive.

How do you find each answer and how do you input it into stat crunch to get the answer

In a normal distribution curve, what percentage of the area under the curve is contained in the region, on one side of the mean, between 1 standard deviation from the mean and 2 standard deviations from the mean?

• A. 95%
• B. 68.27%
• C. 50%
• D. 27.24%%
• E. 13.59%

The tensile strength, X, of a tungsten component is normally distributed with a mean of 546 grams per square centimeter (gscm) and a standard deviation of 50 gscm.

e) What is the 97.1st percentile of tensile strength of our tungsten component in gscm?

f) Suppose we make 3 independent strength measurements of tungsten components. What is the probability that all 3 measurements are at least 500?

g) What is the probability that X is greater than 525 given that X is greater than 500?

h) Suppose X1,X2,,Xk are k independent strength measurements of tungsten components. Let Xbar be the mean of those k values. How large must k be so the variance of the distribution of Xbar equals .8?

3) The following observations are given for two variables.

Y: 5,8,18,20,22,30,10,7

X:2,12,3,6,11,19,18,9

Compute and interpret the sample covariance for the above data.

Compute the standard deviation for x.

Compute the standard deviation for y.

Compute and interpret the sample correlation coefficient.

Let X1, X2, X3 be independent having N(0,1). Let Y1=(X1-X2)/√2, Y2=(X1+X2-2*X3)/√6, Y3=(X1+X2+X3)/√3. Find the joint pdf of Y1, Y2, Y3, and the marginal pdfs.

1) null hypothesis

2) alternative hypothesis

3) where the region of rejection lies (upper tail, lower tail, both tails)

4) the test that is to be used

5) the degrees of freedom

6) the critical value of the test statistic

7) the computed value of the test statistic

8) the statistical decision (whether the null hypothesis is rejected or not)

9) the p-value

10) the assumptions you made in your work

Now, finally - Here is the question:

Trail mix is sold in individual pouches labeled as containing 8 ounces by weight. The weights of 40 pouches are measured (using a tared scale so that only the weight of the trail mix is measured). The sample mean is found to be 8.5 ounces. The sample standard deviation is calculated to be 0.4 ounces. At 95% confidence, is there evidence that the mean weight per pouch is different from 8 ounces?

A research center project involved a survey of 843 internet users. It provided a variety of statistics on internet users.

(a) The sample survey showed that 90% of respondents said the internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the internet has been a good thing for them personally. (Round your answers to four decimal places.)

(b) The sample survey showed that 71% of internet users said the internet has generally strengthened their relationship with family and friends. Develop a 95% confidence interval for the proportion of respondents who say the internet has strengthened their relationship with family and friends. (Round your answers to four decimal places.)

(c) Fifty-seven percent of internet users have seen an online group come together to help a person or community solve a problem, whereas only 25% have left an online group because of unpleasant interaction. Develop a 95% confidence interval for the proportion of internet users who say online groups have helped solve a problem. (Round your answers to four decimal places.)

Please respond with at least 175 words. What are a one tail and a two tailed test. Why are they important and what are their differences?