Question

Consider a paint-drying situation in which drying time for a test specimen is normally distributed with σ = 9. The hypotheses H0: μ = 74 and Ha: μ < 74 are to be tested using a random sample of n = 25 observations.

(a) How many standard deviations (of X) below the null value is x = 72.3? (Round your answer to two decimal places.)

_________________standard deviations

(b) If x = 72.3, what is the conclusion using α = 0.004? Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

z = _____________

P-value = __________

State the conclusion in the problem context.: (choose one)

1)Reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74.

2)Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74.

3)Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 74.

4)Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 74.

(c) For the test procedure with α = 0.004, what is β(70)? (Round your answer to four decimal places.)

β(70) = ______________

(d) If the test procedure with α = 0.004 is used, what n is necessary to ensure that β(70) = 0.01? (Round your answer up to the next whole number.)

n = __________________specimens

Answer #1

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 9. The
hypotheses H0: μ = 74 and
Ha: μ < 74 are to be tested using a
random sample of n = 25 observations.
(a) How many standard deviations (of X) below the null
value is x = 72.3? (Round your answer to two decimal
places.)
standard deviations
(b) If x = 72.3, what is the conclusion using α =
0.004?...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 8. The
hypotheses H0: μ = 73 and
Ha: μ < 73 are to be tested using a
random sample of n = 25 observations.
(a) How many standard deviations (of X) below the null
value is x = 72.3? (Round your answer to two decimal
places.)
standard deviations
(b) If x = 72.3, what is the conclusion using α =
0.003?...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 7. The
hypotheses H0: μ = 73 and
Ha: μ < 73 are to be tested using a
random sample of n = 25 observations.
(a) How many standard deviations (of X) below the null
value is x = 72.3? (Round your answer to two decimal
places.)
____________________standard deviations
(b) If x = 72.3, what is the conclusion using α =
0.002?...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 8. The
hypotheses H0: μ = 73 and
Ha: μ < 73 are to be tested using a
random sample of n = 25 observations.
(a) How many standard deviations (of X) below the null
value is x = 72.3? (Round your answer to two decimal
places.)
standard deviations
(b) If x = 72.3, what is the conclusion using α =
0.006?...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 9. The
hypotheses H0: μ = 75 and
Ha: μ < 75 are to be tested using a
random sample of n = 25 observations.
(a) How many standard deviations (of X) below the null
value is x = 72.3? (Round your answer to two decimal
places.)
standard deviations
(b) If x = 72.3, what is the conclusion using α =
0.005?...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 9. The
hypotheses H0: μ = 73 and
Ha: μ < 73 are to be tested using a
random sample of n = 25 observations.
(a) How many standard deviations (of X) below the null
value is x = 72.3?
(b) If x = 72.3, what is the conclusion using
α = 0.004?
Calculate the test statistic and determine the P-value.
(Round...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 7. The
hypotheses H0: μ = 74 and
Ha: μ < 74 are to be tested using a
random sample of n = 25 observations.
(a) If x = 72.3, what is the conclusion using
α = 0.003?
Calculate the test statistic and determine the P-value.
(Round your test statistic to two decimal places and your
P-value to four decimal places.)
z...

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 8. The
hypotheses H0: μ = 75 and
Ha: μ < 75 are to be tested using a
random sample of n = 25 observations.
(c) For the test procedure with α = 0.004, what is
β(70)? (Round your answer to four decimal places.)

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with σ = 8. The
hypotheses H0: μ = 73 and
Ha: μ < 73 are to be tested using a
random sample of n = 25 observations.
(c) For the test procedure with α = 0.005, what is
β(70)? (Round your answer to four decimal places.)
(d) If the test procedure with α = 0.005 is used, what
n is necessary to ensure that...

Consider the following hypothesis test. Given that n = 84, σ =
8, x = 49.9, and α = 0.01, complete parts a through d below.
H0: μ ≤ 47
HA: μ > 47
a. State the decision rule in terms of the critical value(s) of the
test statistic.
Reject the null hypothesis if the calculated value of the test
statistic, (1)_________ is (2)______________ the critical
value(s),____________ . Otherwise, do not reject the null
hypothesis.
(Round to two decimal places...

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