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A wedding website states that the average cost of a wedding is $26,716. One concerned bride hopes that the average is less than reported. To see if her hope is correct, she surveys 57 recently married couples and finds that the average cost of weddings in the sample was $25,637. Assuming that the population standard deviation is $5388, is there sufficient evidence to support the bride’s hope at the 0.05 level of significance?

A) Yes, reject the null hypothesis.

B) No, fail to reject the null hypothesis.

C) Insufficient information to make a decision.

1 Answer

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Final answer:

To determine whether there is sufficient evidence to support the bride's hope that the average cost of a wedding is less than the reported average, we can conduct a hypothesis test. The null hypothesis is that the average cost of a wedding is equal to the reported average ($26,716), and the alternative hypothesis is that it is less than the reported average. Using a one-sample t-test, we compare the sample mean ($25,637) to the population mean ($26,716) to calculate the t-value. Comparing the t-value to the critical t-value at the 0.05 level of significance, we can reject the null hypothesis and support the bride's hope.

Step-by-step explanation:

To determine whether there is sufficient evidence to support the bride's hope that the average cost of a wedding is less than the reported average, we can conduct a hypothesis test. The null hypothesis is that the average cost of a wedding is equal to the reported average ($26,716), and the alternative hypothesis is that it is less than the reported average. We can compare the sample mean ($25,637) to the population mean ($26,716) using a one-sample t-test.

Using the formula for the t-statistic: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size)), we can calculate the t-value. In this case, the t-value is approximately -1.977.

Using a t-table or a statistical software, we can find the critical t-value for a one-tailed test at the 0.05 level of significance and 56 degrees of freedom (sample size - 1). The critical t-value is approximately -1.673. Since the t-value (-1.977) is less than the critical t-value (-1.673), we can conclude that there is sufficient evidence to support the bride's hope. Therefore, the answer is A) Yes, reject the null hypothesis.

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