Question

The Toylot company makes an electric train with a motor that it
claims will draw an average of only 0.8 ampere (A) under a normal
load. A sample of nine motors was tested, and it was found that the
mean current was *x* = 1.32 A, with a sample standard
deviation of *s* = 0.44 A. Do the data indicate that the
Toylot claim of 0.8 A is too low? (Use a 1% level of
significance.)

What are we testing in this problem?

single mean

single proportion

(a) What is the level of significance?

State the null and alternate hypotheses.

*H*_{0}: *μ* = 0.8;
*H*_{1}: *μ* > 0.8

*H*_{0}: *μ* ≠ 0.8;
*H*_{1}: *μ* =
0.8

*H*_{0}: *p* = 0.8;
*H*_{1}: *p* ≠ 0.8

*H*_{0}: *μ* = 0.8;
*H*_{1}: *μ* ≠ 0.8

*H*_{0}: *p* = 0.8;
*H*_{1}: *p* > 0.8

*H*_{0}: *p* ≠ 0.8;
*H*_{1}: *p* = 0.8

(b) What sampling distribution will you use? What assumptions are
you making?

The standard normal, since we assume that *x* has a
normal distribution with known *σ*.

The Student's *t*, since we assume that *x* has a
normal distribution with unknown *σ*.

The Student's *t*, since we assume
that *x* has a normal distribution with known
*σ*.

The standard normal, since we assume that *x* has a
normal distribution with unknown *σ*.

What is the value of the sample test statistic? (Round your answer
to three decimal places.)

(c) Find (or estimate) the *P*-value.

*P*-value > 0.250

0.125 < *P*-value < 0.250

0.050 < *P*-value < 0.125

0.025 < *P*-value < 0.050

0.005 < *P*-value < 0.025

*P*-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject
or fail to reject the null hypothesis? Are the data statistically
significant at level *α*?

At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are statistically significant.

At the *α* = 0.01 level, we reject the null hypothesis
and conclude the data are not statistically significant.

At the *α* = 0.01 level, we fail to
reject the null hypothesis and conclude the data are statistically
significant.

At the *α* = 0.01 level, we fail to reject the null
hypothesis and conclude the data are not statistically
significant.

(e) Interpret your conclusion in the context of the
application.

There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.

There is insufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.

Answer #1

single mean

alpha = 0.01

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 0.8

Alternative Hypothesis, Ha: μ > 0.8

b)

The Student's t, since we assume that x has a normal distribution
with unknown σ.

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (1.32 - 0.8)/(0.44/sqrt(9))

t = 3.545

c)

P-value Approach

P-value = 0.0038

0.005 < P-value < 0.025

d)

At the α = 0.01 level, we reject the null hypothesis and conclude
the data are statistically significant

e)

There is sufficient evidence at the 0.01 level to conclude that the
toy company claim of 0.8 A is too low.

The Toylot company makes an electric train with a motor that it
claims will draw an average of no more than 0.8 amps under
a normal load. A sample of nine motors were tested, and it was
found that the mean current was x = 1.32 amps, with a
sample standard deviation of s = 0.41 amps. Perform a
statistical test of the Toylot claim. (Use a 1% level of
significance.)
A. What are we testing in this problem?
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