Question

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 78 79 38 94 207 y km/100 14.3 19.2 5.6 11.3 35.9 (a) Verify that Σx = 496, Σy = 86.3, Σx2 = 65,454, Σy2 = 2020.99, Σxy = 11338.5, and r ≈ 0.94513. Σx Σy Σx2 Σy2 Σxy r (b) Use a 1% level of significance to test the claim ρ > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that ρ > 0. Reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is insufficient evidence that ρ > 0. Fail to reject the null hypothesis, there is sufficient evidence that ρ > 0. Correct: Your answer is correct. (c) Verify that Se ≈ 4.3483, a ≈ 0.3050, and b ≈ 0.1709. Se a b (d) Find the predicted distance (km/100) when a drift bottle has been floating for 70 days. (Use 2 decimal places.) km/100 (e) Find a 90% confidence interval for your prediction of part (d). (Use 1 decimal place.) lower limit km/100 upper limit km/100 (f) Use a 1% level of significance to test the claim that β > 0. (Use 2 decimal places.) t critical t Conclusion Reject the null hypothesis, there is sufficient evidence that β > 0. Reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is insufficient evidence that β > 0. Fail to reject the null hypothesis, there is sufficient evidence that β > 0. Correct: Your answer is correct. (g) Find a 95% confidence interval for β and interpret its meaning in terms of drift rate. (Use 2 decimal places.) lower limit upper limit

Answer #1

9.)What is the optimal time for a scuba diver to be on the
bottom of the ocean? That depends on the depth of the dive. The
U.S. Navy has done a lot of research on this topic. The Navy
defines the "optimal time" to be the time at each depth for the
best balance between length of work period and decompression time
after surfacing. Let x = depth of dive in meters, and let
y = optimal time in hours....

Bighorn sheep are beautiful wild animals found throughout the
western United States. Let x be the age of a bighorn sheep
(in years), and let y be the mortality rate (percent that
die) for this age group. For example, x = 1, y =
14 means that 14% of the bighorn sheep between 1 and 2 years old
died. A random sample of Arizona bighorn sheep gave the following
information:
x
1
2
3
4
5
y
13.0
20.5
14.4...

11.4 #7
Let x be a random variable that represents the batting
average of a professional baseball player. Let y be a
random variable that represents the percentage of strikeouts of a
professional baseball player. A random sample of n = 6
professional baseball players gave the following information.
x
0.328
0.270
0.340
0.248
0.367
0.269
y
3.2
7.8
4.0
8.6
3.1
11.1
(a) Find ?x, ?y, ?x2,
?y2, ?xy, and r. (Round
r to three decimal places.)
?x =...

Each box of Healthy Crunch breakfast cereal contains a coupon
entitling you to a free package of garden seeds. At the Healthy
Crunch home office, they use the weight of incoming mail to
determine how many of their employees are to be assigned to
collecting coupons and mailing out seed packages on a given day.
(Healthy Crunch has a policy of answering all its mail on the day
it is received.) Let x = weight of incoming mail and
y...

The correlation coefficient r is a sample statistic.
What does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of ρ yet.
However, there is a quick way to determine if the sample evidence
based on ρ is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of r...

The correlation coefficient r is a sample statistic.
What does it tell us about the value of the population correlation
coefficient ρ (Greek letter rho)? You do not know how to
build the formal structure of hypothesis tests of ρ yet.
However, there is a quick way to determine if the sample evidence
based on ρ is strong enough to conclude that there is some
population correlation between the variables. In other words, we
can use the value of r...

Let x be a random variable that represents the batting
average of a professional baseball player. Let y be a
random variable that represents the percentage of strikeouts of a
professional baseball player. A random sample of n = 6
professional baseball players gave the following information.
x
0.324
0.288
0.340
0.248
0.367
0.269
y
2.6
7.8
4.0
8.6
3.1
11.1
(a) Verify that Σx = 1.836, Σy = 37.2,
Σx2 = 0.572074, Σy2 =
290.38, Σxy = 10.7052, and...

Use the following linear regression equation to answer the
questions.
x3 = ?16.6 + 3.7x1 +
8.6x4 ? 1.9x7
If x4 decreased by 2 units, what would we
expect for the corresponding change in
x3?
(e) Suppose that n = 20 data points were used to construct
the given regression equation and that the standard error for the
coefficient of x4 is 0.924. Construct a 90%
confidence interval for the coefficient of x4.
(Round your answers to two decimal places.)...

Two randomly selected groups of citizens were exposed to
different media campaigns that dealt with the image of a political
candidate. One week later, the citizen groups were surveyed to see
whether they would vote for the candidate. The results were as
follows. Is there sufficient evidence to show a difference in the
effectiveness of the two image campaigns at the 0.05 level of
significance? (Use Conservative - Moderate.)
Exposed to Conservative Image Exposed to Moderate
Image
Number in...

Weatherwise is a magazine published by the American
Meteorological Society. One issue gives a rating system used to
classify Nor'easter storms that frequently hit New England and can
cause much damage near the ocean. A severe storm has an average
peak wave height of μ = 16.4 feet for waves hitting the
shore. Suppose that a Nor'easter is in progress at the severe storm
class rating. Peak wave heights are usually measured from land
(using binoculars) off fixed cement piers....

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