Question

A bank found that in recent years, the average monthly charge on its credit card was $1,350. With an improving economy, they suspect that this amount has increased. A sample of 42 customers resulted in an average monthly charge of $1,375.94 with a standard deviation of $183.78. Do these data provide statistical evidence that the average monthly charge has increased? Formulate the appropriate hypothesis test and draw a conclusion. Use a level of significance of 0.05.

Is there sufficient evidence at the 0.05 level of significance that the average monthly charge has increased?

Determine the null hypothesis, H0, and the alternative hypothesis,H1.

H0:

H1:

(Type whole numbers.)

Compute the test statistic__

(Round to two decimal places as needed.)

Using a level of significance of 0.05, what is the critical value?___

(Round to two decimal places as needed.)

Find the p-value for the test.___

(Round to three decimal places as needed.)

What is your conclusion?

The p-value is ___ the chosen value of α, so____the null hypothesis. There is_____ evidence to conclude that mean is greater than 1,350.

Answer #1

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: μ = 1350

Alternative Hypothesis, Ha: μ > 1350

Test statistic,

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

t = (1375.94 - 1350)/(183.78/sqrt(42))

t = 0.915

Rejection Region

This is right tailed test, for α = 0.05 and df = 41

Critical value of t is 1.68

Hence reject H0 if t > 1.68

P-value Approach

P-value = 0.183

As P-value >= 0.05, fail to reject null hypothesis.

The p-value is greater that the chosen value of α, so fail to reject the null hypothesis. There is not sufficient evidence to conclude that mean is greater than 1,350.

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