An oceanographer claims that the mean dive duration of a North Atlantic right whale is 11.5 minutes. A random sample of 36 dive durations has a mean of 12.4 minutes and a standard deviation of 2.2 minutes. At alphaαequals=0.05 is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. (a) Identify the claim and state Upper H 0H0 and Upper H Subscript aHa. Upper H 0 : nbspH0: ▼ muμ sigmaσ sigma squaredσ2 pp ▼ not equals≠ less than< equals= greater than> greater than or equals≥ less than or equals≤ nothing Upper H Subscript a Baseline : nbspHa: ▼ sigmaσ sigma squaredσ2 muμ pp ▼ greater than> not equals≠ equals= greater than or equals≥ less than or equals≤ less than< nothing (Type integers or decimals. Do not round.) The claim is the ▼ (Blank) null alternative hypothesis. (b) Use technology to find the P-value. Find the standardized test statistic, t. tequals=(Blank) (Round to two decimal places as needed.) Obtain the P-value. Pequals=(Blank) (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. ▼ (Blank) Fail to reject Reject Upper H 0H0 because the P-value ▼ (Blank) is is not greater than alphaα. (d) Interpret the decision in the context of the original claim. There ▼ (Blank) is not is enough evidence at the nothing% level of significance to ▼ (Blank) reject support the claim that the mean dive duration of a North Atlantic right whale is ▼ (Blank) equal to less than greater than or equal to greater than less than or equal to not equal to nothing minutes. (Type integers or decimals. Do not round.) Enter your answer in each of the answer boxes.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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Question

An oceanographer claims that the mean dive duration of a North Atlantic right whale is

11.5

minutes. A random sample of

dive durations has a mean of

12.4

minutes and a standard deviation of

2.2

minutes. At

alphaαequals=0.05

is there enough evidence to reject the oceanographer's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

(a) Identify the claim and state

Upper H 0H0

and

Upper H Subscript aHa.

Upper H 0 : nbspH0:	▼ muμ sigmaσ sigma squaredσ2 pp ▼ not equals≠ less than< equals= greater than> greater than or equals≥ less than or equals≤ nothing
Upper H Subscript a Baseline : nbspHa:	▼ sigmaσ sigma squaredσ2 muμ pp ▼ greater than> not equals≠ equals= greater than or equals≥ less than or equals≤ less than< nothing

(Type integers or decimals. Do not round.)

The claim is the

▼

(Blank)

null

alternative

hypothesis.

(b) Use technology to find the P-value. Find the standardized test statistic, t.

tequals=(Blank)

(Round to two decimal places as needed.)

Obtain the P-value.

Pequals=(Blank)

(Round to three decimal places as needed.)

▼

(Blank)

Fail to reject

Reject

Upper H 0H0

because the P-value

▼

(Blank)

is not

greater than

alphaα.

(d) Interpret the decision in the context of the original claim.

There

▼

(Blank)

is not

enough evidence at the

nothing%

level of significance to

▼

(Blank)

reject

support

the claim that the mean dive duration of a North Atlantic right whale is

▼

(Blank)

equal to

less than

greater than or equal to

greater than

less than or equal to

not equal to

nothing

minutes.

(Type integers or decimals. Do not round.)

Enter your answer in each of the answer boxes.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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