The accompanying table contains data on the weight, in grams, of a sample of 50
ID: 3236465 • Letter: T
Question
The accompanying table contains data on the weight, in grams, of a sample of 50 tea bags produced during an eight-hour shift. Complete parts (a) through (d).
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Click the icon to view the data table.
a. Is there evidence that the mean amount of tea per bag is different from
5.5
grams? (Use
alpha
equals0.05
.)
State the null and alternative hypotheses.
Upper H 0
:
mu
equals
0
Upper H 1
:
mu
not equals
0
(Type integers or decimals.)
Determine the test statistic.
The test statistic is
nothing
.
(Round to two decimal places as needed.)
Find the p-value.
p-valueequals
nothing
(Round to three decimal places as needed.)
State the conclusion.
Reject
Do not reject
Upper H 0
.
There is
insufficient
sufficient
evidence to conclude that the mean difference is not equal to
5.5
inches.
b. Construct a
95
%
confidence interval estimate of the population mean amount of tea per bag. Interpret this interval.
The
95
%
confidence interval is
nothing
less than or equalsmuless than or equalsnothing
.
(Round to four decimal places as needed.)
Interpret the
95
%
confidence interval. Choose the correct answer below.
A.
Do not reject
Upper H 0
because the hypothesized mean
is not
contained within the confidence interval.
B.
Reject
Upper H 0
because the hypothesized mean
is
contained within the confidence interval.
C.
Reject
Upper H 0
because the hypothesized mean
is not
contained within the confidence interval.
D.
Do not reject
Upper H 0
because the hypothesized mean
is
contained within the confidence interval.
c. Compare the conclusions reached in (a) and (b). Choose the correct answer below.
A.
The confidence interval shows insufficient evidence while the hypothesis test shows sufficient evidence that the mean amount of tea per bag is different from
5.5
grams.
B.
The confidence interval shows sufficient evidence while the hypothesis test shows insufficient evidence that the mean amount of tea per bag is different from
5.5
grams.
C.
The confidence interval and hypothesis test both show that there is
sufficient
evidence that the mean amount of tea per bag is different from
5.5
grams.
D.
The confidence interval and hypothesis test both show that there is
insufficient
evidence that the mean amount of tea per bag is different from
5.5
grams.
Click to select your answer(s).
5.65
5.42
5.41
5.42
5.52
5.36
5.52
5.43
5.52
5.42
5.57
5.41
5.52
5.55
5.55
5.62
5.57
5.44
5.43
5.52
5.47
5.39
5.49
5.63
5.52
5.31
5.65
5.29
5.48
5.57
5.78
5.58
5.43
5.57
5.59
5.48
5.33
5.48
5.53
5.57
5.59
5.47
5.44
5.27
5.55
5.61
5.49
5.58
5.67
5.37
Explanation / Answer
Solution
Let Xi = weight (in grams) of the ith sample tea bag.
X ~ N(µ, ^2) and is unknown
Hypotheses:
Null H0: µ = µ0 =
5.5
Alternative HA: µ
5.5
Test Statistic:
t = (n)(Xbar - µ0)/s where
n = sample size =
50
Xbar = sample mean =
5.4925
µ0 (given) =
5.5
s = sample standard deviation =
0.079794
So, tcal = - 0.66
|tcal| = 0.66
p-value of tcal =
0.509408
Conclusion
Since p-value > level of significance (0.05), H0 is accepted.
Hence, there is sufficient evidence to suggest that the mean weight of tea bags is 5.5 grams
DONE
Hypotheses:
Null H0: µ = µ0 =
5.5
Alternative HA: µ
5.5
Test Statistic:
t = (n)(Xbar - µ0)/s where
n = sample size =
50
Xbar = sample mean =
5.4925
µ0 (given) =
5.5
s = sample standard deviation =
0.079794
So, tcal = - 0.66
|tcal| = 0.66
p-value of tcal =
0.509408
Conclusion
Since p-value > level of significance (0.05), H0 is accepted.
Hence, there is sufficient evidence to suggest that the mean weight of tea bags is 5.5 grams
DONE
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