Question

Consider a paint-drying situation in which drying time for a
test specimen is normally distributed with *σ* = 9. The
hypotheses *H*_{0}: *μ* = 75 and
*H*_{a}: *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?

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 |
= | |

-valueP |
= |

State the conclusion in the problem context.

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

75.Reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean drying time is less than 75.

Do not reject the null hypothesis. There is sufficient evidence to conclude that the mean drying time is less than 75.

(c) For the test procedure with *α* = 0.005, what is
*β*(70)? (Round your answer to four decimal places.)

*β*(70) =

(d) If the test procedure with *α* = 0.005 is used, what
*n* is necessary to ensure that *β*(70) = 0.01?
(Round your answer up to the next whole number.)

specimens

(e) If a level 0.01 test is used with *n* = 100, what is the
probability of a type I error when *μ* = 76? (Round your
answer to four decimal places.)

Answer #1

(a)

**Answer: 1.5 standard deviations**

(b)

**Conclusion:** Do not reject the null hypothesis.
There is not sufficient evidence to conclude that the mean drying
time is less than 75.

(c)

(d)

(e)

Probability of type I error will be

P(z < -4.11) = 0.0000

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 = 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 = 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 = 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 = 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 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 the following hypothesis test.H0: μ = 15Ha: μ ≠ 15A sample of 50 provided a sample mean of 14.11. The population
standard deviation is 3.(a)Find the value of the test statistic. (Round your answer to two
decimal places.)(b)Find the p-value. (Round your answer to four decimal
places.)p-value =(c)Atα = 0.05,state your conclusion.Reject H0. There is sufficient evidence to
conclude that μ ≠ 15.Reject H0. There
is insufficient evidence to conclude that μ ≠
15. Do not rejectH0. There is sufficient...

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