Assume that​ women's heights are normally distributed with a mean given by mu equals 62.1 in​, and a standard deviation given by sigma equals 2.7 in. ​(a) If 1 woman is randomly​ selected, find the probability that her height is less than 63 in. ​(b) If 32 women are randomly​ selected, find the probability that they have a mean height less than 63 in.

As part of a study of wheat maturation, an agronomist selected a sample of wheat plants at random from a field plot. For each plant, the agronomist measured the moisture content from two locations: one from the central portion and one from the top portion of the wheat head. The agronomist hypothesizes that the central portion of the wheat head has more moisture than the top portion. What can the agronomist conclude with α = 0.01? The moisture content data are below.

central	top
62.7 63.6 60.9 63.1 62.7 63.7 62.5	61.7 62.7 60.2 62.5 61.6 62.8 62.3

a) What is the appropriate test statistic?
---Select--- na, z-test, One-Sample t-test, Independent-Samples t-test, Related-Samples t-test

b)
Condition 1:
---Select--- top portion wheat maturation moisture content wheat head central portion
Condition 2:
---Select--- top portion wheat maturation moisture content wheat head central portion

c) Compute the appropriate test statistic(s) to make a decision about H₀.

critical value =  ; test statistic =
Decision:  ---Select--- Reject H0, Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below. (Please say if "na")
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ; ---Select--- na, trivial effect, small effect, medium effect, large effect
r² =  ; ---Select--- na, trivial effect, small effect, medium effect, large effect

f) Make an interpretation based on the results. (select one)

-The central portion of the wheat head had significantly more moisture than the top portion.

-The central portion of the wheat head had significantly less moisture than the top portion.    

-There was no significant moisture difference between the central and top portion of the wheat head

Quantitative noninvasive techniques are needed for routinely assessing symptoms of peripheral neuropathies, such as carpal tunnel syndrome (CTS). An article reported on a test that involved sensing a tiny gap in an otherwise smooth surface by probing with a finger; this functionally resembles many work-related tactile activities, such as detecting scratches or surface defects. When finger probing was not allowed, the sample average gap detection threshold for m = 7 normal subjects was 1.85 mm, and the sample standard deviation was 0.57; for n = 11 CTS subjects, the sample mean and sample standard deviation were 2.47 and 0.85, respectively. Does this data suggest that the true average gap detection threshold for CTS subjects exceeds that for normal subjects? State and test the relevant hypotheses using a significance level of 0.01. (Use μ₁ for normal subjects and μ₂ for CTS subjects.)

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on distances. An article reported that in one investigation, six sites along interstate highways where service signs are posted were selected. For each site, crash data was obtained for a three-year period before distance information was added to the service signs and for a one-year period afterward. The number of crashes per year before and after the sign changes were as follows.

Before:	15	23	65	121	66	65
After:	16	21	43	83	79	74

a)The article included the statement "A paired t test was performed to determine whether there was any change in the mean number of crashes before and after the addition of distance information on the signs." Carry out such a test. [Note: The relevant normal probability plot shows a substantial linear pattern.]
State and test the appropriate hypotheses. (Use

α = 0.05.)

Calculate the test statistic and P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
P-value	=

b)If a seventh site were to be randomly selected among locations bearing service signs, between what values would you predict the difference in number of crashes to lie? (Use a 95% prediction interval. Round your answers to two decimal places.)

A technician compares repair costs for two types of microwave ovens (type I and type II). He believes that the repair cost for type I ovens is greater than the repair cost for type II ovens. A sample of 5959 type I ovens has a mean repair cost of $73.27$⁢73.27, with a standard deviation of $10.76$⁢10.76. A sample of 4747 type II ovens has a mean repair cost of $69.22$⁢69.22, with a standard deviation of $23.21$⁢23.21. Conduct a hypothesis test of the technician's claim at the 0.050.05 level of significance. Let μ1μ1 be the true mean repair cost for type I ovens and μ2μ2 be the true mean repair cost for type II ovens.

Step 2 of 4 :

Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 4: Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places

Step 4 of 4: Make the decision for the hypothesis test. Fail or reject to fail.

Consider the data.

xi	3	12	6	20	14
yi	55	35	45	10	15

The estimated regression equation for these data is ŷ = 62.25 − 2.75x.

(a) Compute SSE, SST, and SSR using equations SSE = Σ(y_i − ŷ_i)², SST = Σ(y_i − y)², and SSR = Σ(ŷ_i − y)².

SSE=

SST=

SSR=

(b) Compute the coefficient of determination r².(Round your answer to three decimal places.)

r² =

Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) Chose one of the following.

1.The least squares line provided a good fit as a large proportion of the variability in y has been explained by the least squares line.

2.The least squares line did not provide a good fit as a large proportion of the variability in y has been explained by the least squares line.    

3.The least squares line provided a good fit as a small proportion of the variability in y has been explained by the least squares line.

4.The least squares line did not provide a good fit as a small proportion of the variability in y has been explained by the least squares line.

(c) Compute the sample correlation coefficient. (Round your answer to three decimal places.)

A plant physiologist investigated the effect of flooding on root metabolism in two tree

species: flood-tolerant river birch and the intolerant European birch. Four seedlings of

each species were flooded for one day, and four were used as controls. The concentration

of adenosine triphosphate (ATP) in the roots of each plant was measured. The data (nmol

ATP per mg tissue) as shown in the table.

River birch European Birch

Flooded Control Flooded Control  

	1.45	1.70	0.21	1.34
	1.19	2.04	0.58	0.99
	1.05	1.49	0.11	1.17
	1.07	1.91	0.27	1.30
Mean	1.19	1.785	0.2925	1.20

For these data, SS(species of birch)=2.19781, SS(flooding)=2.25751, SS(interaction)=0.097656,

and SS(within)=0.47438.

i. Construct the ANOVA table, include p-values.

iii. What is the F test statistic and its degrees of freedom for testing that species has no

effect on ATP concentration?

Consider the daily percent changes of McDonald’s stock price and those of the Dow

Jones Industrial Average for trading days in the months of July and August 1987.

Data can be found in the Excel file S4.XLSX (Mc-Dow) in the Excel directory.

a. Draw a scatterplot of McDonald’s daily percent changes against the Dow Jones

percent changes.

b. Describe the relationship you see in this scatterplot.

c. Find the correlation between these percent changes. Does this agree with your

impression of the scatterplot?

d. Find the coefficient of determination (you may just square the correlation).

Interpret this number as “variation explained”. In financial terms, it represents

the proportion of non-diversifiable risk in McDonald’s. For example, if it were

100%, McDonald’s stock would track the market perfectly, and diversification

would introduce nothing new.

e. Find the proportion of diversifiable risk. This is just 1 - R2 (or 100% minus the

percentage of non-diversifiable risk). This indicates the extent to which you

can diversify away the risk of McDonald's stock by investing part of your

portfolio in the Dow Jones Industrial stocks.

f. Find the regression equation to predict the percent change in McDonald's stock

from the percent change in the Dow Jones Index. Identify the stock's so-called

beta, a measure used by market analysts, which is equal to the slope of this

line. According to the capital asset pricing model, stocks with large beta values

tend to give larger expected returns (on average, over time) than stocks with

smaller betas.

g. Find the 95% confidence interval for the slope coefficient.

h. Test at the 5% level to see whether or not the daily percent changes of

McDonald's and of the Dow Jones Index are significantly associated.

i. Test at the 5% level to see whether the beta of McDonald's is significantly

different from 1, which represents the beta of a highly diversified portfolio

McDonald’s stock vs Dow Jones
Dow Jones	McDonald’s
0.47	1.12
1.41	-0.29
0.70	0.83
0.69	0.58
-0.69	-0.52
-1.38	0.20
-2.34	-0.12
1.44	1.16
-0.24	0.10
0.47	0.53
-1.18	0.52
-1.19	-0.89
0.72	-0.80
0.72	0.09
0.95	0.07
0.94	0.54
0.93	0.35
0.92	1.04
0.92	0.78
0.45	1.10
0.23	0.18
-1.35	-0.58
-1.14	-0.41
2.08	0.78
3.17	1.07
-0.66	-0.09
1.99	1.69
3.03	1.69
-0.84	-0.42
1.48	0.83
-0.63	-0.23
2.31	0.56
-0.21	-1.70
-2.06	0.42
0.84	1.54
0.00	0.10
-2.08	-0.46
2.34	0.94
-0.21	0.76
-1.67	-0.99
-2.33	-1.33
1.08	0.89

1. The average height of adult females in the United States is 64.5 inches. Assume that σ = 2.8 inches and the distribution is approx. normal.
   1. Find the probability that a female selected at random is taller than 66 inches.
   2. If a sample of 25 females is selected, find the probability that their mean height would be taller than 66 inches.
   3. Which probability is smaller? What can you say about the variability of the average of sample vs. the variability of a single observation?

A toll-free phone number is available from 9 a.m. to 9 p.m. for your customers to register complaints about a product purchased from your company. Past history indicates that an average of 1.0 calls are received per minute. Complete parts (a)through (c).

A.    what is the probability that during a 1 min period zero phone calls will be received?

B.    what is the probability that during a 1 min period three or more phone calls will be received?

C.    what is the maximum number of phone calls that will be received in a 1 min period 99.99% of the time?

30. In an effort to make a healthier product, the Oriental Spice Sauce company has reduced the amount of sodium in their product to 800mg. In addition, the standard deviation of the amount of sodium should be 80. To make sure this new product continues to meet the standard, a random sample of 24 bottles is taken, and the standard deviation for the sample was 120.7812. Is there evidence at α=0.025 that the standard deviation of the sodium content exceeds the desired level? Assume the population is normally distributed.

Step 1 of 5: State the null and alternative hypotheses. Round to four decimal places when necessary.

H0:

Ha:

Step 2 of 5: Determine the critical value(s) of the test statistic. If the test is two-tailed, separate the values with a comma. Round your answer to three decimal places.

Step 3 of 5: Determine the value of the test statistic. Round your answer to three decimal places.

Step 4 of 5: Make the decision.

A. Reject Null Hypothesis

B. Fail to Reject Null Hypothesis

Step 5 of 5: What is the conclusion?

A. There is sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

B. There is not sufficient evidence to show that the standard deviation of the sodium content exceeds the desired level.

CASE STUDY /big 4 Consultants has been appointed by a leading group in hotel industry to prepare feasibility report for opening a five-star hotel in Ras al Khaima. The group had been most successful one in the hotel industry and had always kept its eyes open for new opportunities.

In view of the very fast industrial growth in the city of Ras al Khaima, the city had attracted the attention of the group. It is historically known as Julfar, is one of the seven emirates that make up the United Arab Emirates (UAE). Its name could be taken to mean "headland of the small huts", which can be attributed to the indigenous buildings that existed along the coast. The Emirate is in the northern part of the UAE, bordering Oman’s exclave of Musandum. RAK, apart from being a developing city, has added advantage of pleasant weather and several places of tourist attraction in the neighborhood. Moreover, the closeness to Dubai and Abudhabi, a city of international stature, has made it very easily accessible to international tourists.

For this Consultancy, this was the first time in this area that an assignment concerning hotel industry had been received. They, however, soon realized that the assignment was not as simple as it appeared to be in the first place. The feasibility of such a hotel would depend essentially on two factors. Businessman visiting the city for work would constitute one segment of the market, while tourists would constitute the other. Further, the tourists could be from UAE or foreigners. The success of such a hotel would also depend upon the relative attraction of other tourist centres in the vicinity. Further, it was necessary to estimate fluctuations in demand for hotel accommodation so that attractive discounts could be offered during the off-season for business conferences, executive developmental programmes, etc.

The consultants realized that they would have to undertake a market research on a national scale to assess the tourist potential of the city. They would also have to survey the foreign tourists to estimate one of the most important segments of the market. They wondered whether such a survey will have to extend over a period of one full year to completely take into account the seasonal variations in tourists’ traffic. Moreover, they were undecided about the manner in which survey should be conducted. The company also feared that in absence of an accurate definition of the problem, they may land up surveying the complete tourist market in UAE rather than studying feasibility of a hotel in RAK.

Thus, the problem appeared well defined and that they were concerned as the preliminary report explaining methodology of the research and the questionnaires to be used to be submitted to the client along with the estimate of expenses within one month.

QUESTIONS

1. Apply your ideas in defining the problem of assessing feasibility of hotel in RAK so as

    to help designing the survey.

2. It is important to plan a survey for collecting information on expected demand for

    hotel space. Illustrate.

3. Being the coordinator of this research at Big 4 Consultants, explain various steps you

    would suggest to your research team in preparing the report to the Hotel management.

A random sample of 880 births included 433 boys. Use a 0.10 significance level to test the claim that 50.8% of newborn babies are boys. Do the results support the belief that 50.8% of newborn babies are​ boys?

The data below are the average monthly temperatures, in °F, and the monthly natural gas consumption, in ccf, for a household in northwestern Pennsylvania.

a.)Test the significance of the correlation coefficient using α = 0.05 and the claim ρ < 0. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision

b.) Find the equation of the regression line for the given data

	Temperature		47	35	21	27	39	48	61	65	70
	Consumption		34	169	248	134	137	100	19	34	12