Question

The data table below contains the amounts that a sample of nine customers spent for lunch? (in dollars) at a? fast-food restaurant. Complete parts? (a) through? (c). Click here to view page 1 of the table of critical values of t. LOADING... Click here to view page 2 of the table of critical values of t. LOADING... 4.21 4.21 4.99 4.99 5.98 5.98 6.51 6.51 7.43 7.43 7.41 7.41 8.44 8.44 8.43 8.43 10.07 10.07 a. At the 0.10 0.10 level of? significance, is there evidence that the mean amount spent for lunch is different from ?$ 6.50 6.50?? State the null and alternative hypotheses. Upper H 0 H0?: mu ? ? greater than > equals = not equals ? less than < greater than or equals ? less than or equals ? nothing Upper H 1 H1?: mu ? ? not equals ? less than < greater than or equals ? less than or equals ? equals = greater than > nothing ?(Type integers or decimals. Do not include the? $ symbol in your? answer.) Identify the critical? value(s). The critical? value(s) is(are) nothing . ?(Round to four decimal places as needed. Use a comma to separate answers as? needed.) Determine the test statistic. The test statistic is nothing . ?(Round to four decimal places as? needed.) State the conclusion. ? Reject Do not reject Upper H 0 H0. There is ? sufficient insufficient evidence to conclude that the mean amount spent for lunch is different from ?$ 6.50 6.50. b. What assumption must you make about the population distribution in order to conduct the t test in? (a)? A. The population distribution of the amount spent follows the? Student's t distribution. B. The population distribution of the amount spent is skewed to one side. C. The population distribution of the amount spent is normally distributed. c. Because the sample size is? 9, do you need to be concerned about the shape of the population distribution when conducting the t test in? (a)? Explain. Choose the correct answer below. A. With a small sample? size, it is difficult to evaluate the assumption of normality.? However, the distribution may be symmetric because the mean and the median are close in value. B. With a small sample? size, it is difficult to evaluate the assumption of a skewed distribution.? However, the distribution may be asymmetric because the mean and the median are not close in value. C. With a small sample? size, it is difficult to evaluate the assumption that the distribution follows the? Student's t distribution.? However, the distribution may be symmetric because the mean and the median are close in value.

Answer 1

The test statistics is given by

Now, from the given data

assuming H₀ is true, the test statistics is

The critical values for t₈ at 0.10 critical level are -1.8595,1.8595

As test statistics lies between the critical value, we do not have sufficient evidence to reject H₀.

Do not reject H₀. There is insufficient evidence to conclude that the mean amount spent for lunch is different from 6.50.

A. The population distribution of the amount spent follows the Student's t distribution.

A. With a small sample size, it is difficult to evaluate the assumption of normality. However, the distribution may be symmetric because the mean and the median are close in value.