Im am so lost....
A bank conducts a survey in which it randomly samples 400 of it customers. The survey asks the customers which way they use the bank the most, (1) interacting with teller, (2)atm use, (3) internet bank service. It was also asked their level of satifaction on the service they mostly used. (on a scale from 0 to 10, 0 being poor and 10 being excellent) does this mean satifaction differ according to how they most use the bank?
A) Identifing notation, state the null and alternitive hypotheses for conducting an ANOVA with data from the survey?
B) Report the df values for this ANOVA, about what range of f test statistic values give the p values below 0.05?
C) For the data, F=0.046 and P=0.63, what can you conclude?
D) What were the assumptions on which the ANOVA was based, which assumptions is most important?
a) µ1= interacting with teller at bank, µ2= using ATMs, µ3= using bank’s internet service H0: µ1= µ2= µ3 vs Ha: at least one of the means is different from the others
b) d.f.G. = 3-1=2 degrees of freedom; d.f.E = 400-3 = 397;
For this combination of degrees of freedom, an F value greater than about 3.0185 will give a p-value below 0.05.
c) A normal level of significance for hypothesis testing is either 0.05 and 0.01. Since the p-value is 0.63, we are unable to reject the null hypothesis. We don’t have enough evidence to support a claim that the mean satisfaction levels for the three types of customers are different from each other. To conclude, the mean satisfaction level doesn’t differ for how customers use the bank.
A) Null hypothesis: The satisfaction level does not differ according to how the customers most use the bank.
Alternative hypothesis: The satisfaction level differs according to how the customers most use the bank.
B) The df values for this ANOVA would depend on the specifics of the survey, such as the number of groups being compared. Without that information, it is not possible to provide an accurate df value range for the F test statistic to have p values below 0.05.
C) With F=0.046 and P=0.63, it can be concluded that there is no significant difference in satisfaction levels based on how the customers most use the bank.
D) The assumptions on which the ANOVA is based include:
1) The data is normally distributed within each group.
2) Homogeneity of variance - the variances of the groups being compared are equal.
3) Independence - the observations within each group are independent.
Among these assumptions, the assumption of normality is usually considered the most important.
A) The null hypothesis for conducting an ANOVA with data from the survey would be that satisfaction levels are the same across all three ways customers use the bank the most. The alternative hypothesis would be that satisfaction levels differ according to how customers most use the bank.
B) To report the df values for this ANOVA, we need more information about the design of the survey and the number of factors being considered. In a one-way ANOVA with three groups, the df values would be (2, 397), where 2 represents the number of groups minus 1, and 397 represents the total number of customers sampled minus the number of groups.
Regarding the range of F test statistic values that give p values below 0.05, it depends on the degrees of freedom values and the alpha level chosen for the test. Typically, with higher degrees of freedom, smaller F values would be needed to achieve a significant p value.
C) With F = 0.046 and P = 0.63, we can conclude that there is not enough evidence to reject the null hypothesis. This suggests that satisfaction levels do not significantly differ based on how customers use the bank the most.
D) The assumptions on which the ANOVA is based include independence of observations, normality of the distribution within each group, and equal variances across groups. Among these assumptions, the equal variances assumption (also known as homogeneity of variances) is often considered the most important.
I can help you break down and understand the questions step by step:
A) To conduct an ANOVA with data from the survey, we first need to state the null and alternative hypotheses. In this case, the null hypothesis (H0) would be that satisfaction does not differ according to how customers use the bank. The alternative hypothesis (Ha) would be that satisfaction does differ depending on the way customers use the bank.
B) To report the degrees of freedom (df) values for this ANOVA, we need to know the number of groups or categories being compared and the total number of observations. In this case, there are 3 ways that customers use the bank (interacting with teller, ATM use, and internet bank service), so there would be 3 - 1 = 2 degrees of freedom between groups. The total number of observations is 400 customers, so the degrees of freedom within groups would be 400 - 3 = 397.
The range of F-test statistic values that would give p-values below 0.05 depends on the degrees of freedom values and the significance level chosen for the test. Typically, a p-value below 0.05 is considered statistically significant, indicating that there is evidence to reject the null hypothesis.
C) For the given data, F = 0.046 and P = 0.63. Based on the p-value of 0.63, which is greater than 0.05, we would fail to reject the null hypothesis. Therefore, we cannot conclude that satisfaction differs according to how customers use the bank.
D) The assumptions on which the ANOVA is based include:
1. Independence of observations: Each observation (customer satisfaction rating) should be independent of others.
2. Normality: The population distributions should be approximately normal within each group.
3. Homogeneity of variances: The variances of each group should be approximately equal.
Among these assumptions, the assumption of independence is typically the most important. Violation of independence can lead to biased and unreliable results.