# Hypothesis Test on Bank Service Ratings

• toothpaste666
In summary, the bank conducted a survey among its customers and found that out of 505 respondents, 258 rated their overall services as excellent. A statistical test was performed to determine if the proportion of customers who would rate the services as excellent is significantly different from 46%. The test resulted in a Z-score of 2.29 and a corresponding p-value of 0.022. This indicates that there is strong evidence to reject the null hypothesis and conclude that the proportion is not equal to 46%.
toothpaste666

## Homework Statement

An independent bank, concerned about its customer base, decided to conduct a survey of bank customers. Out of 505 customers who returned the survey form, 258 rated the overall bank services as excellent.

(a) Test, at level α = .10, the null hypothesis that the proportion of customers who would rate the overall bank services as excellent is .46 versus a two-sided alternative

(b) Calculate the p-value and comment on the strength of evidence.

## The Attempt at a Solution

a) the proportion of customers in the sample who rated the service as excellent is
258/505
the null hypothesis is that μ = .46. The alternatives are that μ < .46 or μ > .46. we reject the null when Z> 1.645 or Z < -1.645

Z = (X-μ)sqrt(n)/s = (258/505 - .46)sqrt(505)/s

but I am running into a problem because I don't know s so I am wondering if I did this wrong?

Normally, the variance for proportions is (p)(1-p).
So the corresponding s is ##\sqrt{p(1-p)}##.
And from my understanding, you would want to use the p from your null hypothesis rather than the p from your sample.

ok I was looking at the wrong chapter of my book. It is a large sample so we use the statistic
H0 : p = p0
H1 : p ≠ p0
Z = (x-np0)/sqrt(np0(1-p0)) = (258 - 505(.46))/sqrt(505(.46)(.54)) = 2.29
we reject H0 if Z > zα/2 or Z < -zα/2
zα/2 = z.1/2= z.05 = 1.645
Z > zα/2 so we reject the null hypotheses. They are not equal.

for part b)
P(Z>2.29) = 1 - F(2.29) = 1 - .9890 = .011
since it is a two sided test, the p value is twice this
the p value is .022

## 1. What is a hypothesis test?

A hypothesis test is a statistical method used to determine whether there is a significant difference between two or more groups or variables. It is used to test the validity of a hypothesis or claim by analyzing sample data.

## 2. How is a hypothesis test on bank service ratings conducted?

A hypothesis test on bank service ratings typically involves collecting a sample of data from customers who have used the bank's services. The data is then analyzed using statistical methods to determine if there is a significant difference in ratings between different groups, such as different branches or different types of services.

## 3. Why is a hypothesis test important for bank service ratings?

A hypothesis test is important for bank service ratings because it allows for a more objective evaluation of the bank's performance. It can help identify areas where the bank may need to improve and provide insights into customer satisfaction levels.

## 4. What are some factors that can affect the results of a hypothesis test on bank service ratings?

Some factors that can affect the results of a hypothesis test on bank service ratings include the sample size, the selection of participants, and the accuracy of the data collected. It is important to carefully design and conduct the test to ensure accurate and reliable results.

## 5. How can the results of a hypothesis test on bank service ratings be interpreted?

The results of a hypothesis test on bank service ratings can be interpreted by comparing the calculated p-value to a predetermined significance level. If the p-value is less than the significance level, it can be concluded that there is a significant difference in ratings between the groups being compared. If the p-value is greater than the significance level, it can be concluded that there is not enough evidence to reject the null hypothesis and there is no significant difference in ratings.

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