According to a money report by a government​ institution, 18-to-20-year-old college students have an average credit card balance of​ $569.A researcher wants to find out if this number is lower now and collects data for a random sample o f40 college students. Their average credit card debt was found to be​ $540 with a sample standard deviation of​ $67.93. Complete parts a through c. Using α=0.05​, does this sample provide enough evidence to conclude that the average credit card balance of​ 18-to-20-year-old college students has decreased since​ 2016? Determine the null and alternative hypotheses. H0​: μ▼= ≥ ≤ = ≠ H1​: μ ▼ = ≥ ≤ ≠ Calculate the appropriate test statistic. tx= enter your response here ​(Round to two decimal places as​ needed.) Part 4 State the conclusion. ▼ H0. There▼ is not is sufficient evidence to conclude that the average credit card balance of​ 18-to-20-year-old college students has changed increased decreased stayed the same since 2016. Part 5 b. Does changing the value of α from 0.05 to 0.01 affect the​ conclusion? Why or why​ not? The conclusion should stay as nonrejection stay as rejectionchange to nonrejectionchange to rejectionbecause the test statistic is ▼greater thanless thanequal to▼ t Subscript alpha divided by 2tα/2t Subscript alphatαnegative t Subscript alpha−tα=enter your response here. ​(Round to three decimal places as​ needed.) Part 6 c. Determine the precise​ p-value for this test using Excel. The​ p-value is enter your response here.

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