a a a 1
Homework 13
Question 40: Enter the data into your calculator or computer p-value
Question 41: a alpha = 0.05
Decision: we reject the null hypothesis
Conclusion: there is no sufficient evidence to affirm the sample data set.
Question 42: alpha = 0.01
Decision: we reject the null hypothesis
Conclusion: there is no substantial evidence to affirm the sample data set.
Question 43: Name one assumption that must be true
The population of each of the samples are normally distributed
Question 44: what is the other assumption that must be true
The samples are independent from one another
Question 45: State the null and alternative hypotheses
Null hypothesis: σ1 = σ2
Alternative hypothesis: σ1 < σ2
Question 46: What is s1 in this problem?
S2 = 2.01
Question 47: What is s2 in this problem?
S2 = 4.11
Question 51: Is the claim accurate
The claim is not accurate. This is because at 10% level of significance the null hypothesis
is not rejected and the data do not show that the variations in drive times for the first
worker is less that the variations in drive times for the second worker
Question 52: State the null and alternative hypotheses
Null hypothesis: 𝜎1
2= 𝜎2
2
Alternative hypothesis: 𝜎1
2< 𝜎2
2
Question 53: What is the F statistic
F- statistic = 2.8675
Question 59: State SSbetween, SSwithin, and F statistic
a a a 2
F statistic = 0.265
SSbetween = 26
SSwithin = 441
Question 62: degrees of freedom – denominator: df (denom)
Df (denom) =15
Question 64: Using a significance level of 10%, test the hypothesis that the three
formulas produce the same mean weight gain
Null hypothesis: µL = µT = µJ
Alternative hypothesis: µL ≠ µT ≠ µJ
Degree of freedom (df) = 2
p-value = 0.5304; under 5% level of significance. Therefore, do not reject the null
hypothesis.
Question 68: Assume that all distributions are normal, the four population standard
deviations are approximately the same, and the data were collected independently and
randomly. Use a level of significance of 0.05
p-value = 07435; under 5% significance level. Therefore, we accept the null hypothesis.
Question 70: Assume that all distributions are normal, the four population standard
deviations are approximately the same, and the data were collected independently and
randomly. Use a level of significance of 0.05
p-value = 0.6571; under 5% significance level. Therefore, we accept the null hypothesis
Question 73:
The data from the chart appear to be normally distributed.
Null hypothesis: μ1 = μ2 = μ3
Alternative hypothesis: μ1 ≠ μ2 ≠ μ3
P-value = 0.0004; under 1% level of significance. Therefore, we reject the null hypothesis
as the evidence is sufficient to affirm that the number of eggs laid in 14 days is equal in
all samples.
Question 77: Which two magazine types do you think have the same variance in
length
Home decorating and news magazines
a a a 3
Question 79: Is the variance for the amount of money, in dollars, that shoppers spend
on Saturdays at the mall the same as the variance for the amount of money that
shoppers spend on Sundays at the mall?
Null hypothesis: 𝜎1= 𝜎2
Standard deviation (Saturday)= 42.67
Standard deviation (Sunday) = 36.80
P- value = 0.00367; under 5% level of significance. Therefore, we reject the null
hypothesis.
Question 86:
Null hypothesis: μ ≥ 129
Alternative hypothesis: μ < 129
The t-test = 1.209 with a p-value of 0.8792 under a 5% significance level. Therefore,
there is sufficient evidence not to reject the null hypothesis.
