Consider the following hypothesis test: H0: μ = 18 Ha: μ ≠ 18 A sample of 48 provided a sample mean x = 17 and a sample standard deviation s = 4.9. a. Compute the value of the test statistic (to three decimal places.) b. Use the t distribution table (Table 2 in Appendix B) to compute a range for the p-value. (to two decimal places) p-value is between is c. At α = .05, what is your conclusion? p-value is Selectgreater than or equal to 0.05, rejectgreater than 0.05, do not rejectless than or equal to 0.05, do not rejectless than 0.05, rejectequal to 0.05, do not rejectnot equal to 0.05, do not rejectItem 4 H0 d. What is the rejection rule using the critical value? Reject H0 if t is Selectgreater than or equal to -2.012greater than 2.012less than or equal to -2.012less than -2.012equal to 2.012not equal to -2.012Item 5 or t is Selectgreater than or equal to 2.012greater than -2.012less than or equal to 2.012less than -2.012equal to 2.012not equal to -2.012Item 6 What is your conclusion? t = ; Selectdo not rejectrejectItem 8 H0
Here
sample mean
sample standard deviation
and sample size
The test statistic can be written as
which under H0 follows a t distribution with n-1 df.
We reject H0 at 5% level of significance if or P-value < 0.05
Now,
The value of the test statistic
and critical value
and P-value
Since P-value > 0.05 and , so we fail to reject H0 at 5% level of significance and we can conclude that the population mean is not significantly different from 18.
Consider the following hypothesis test: H0: μ = 18 Ha: μ ≠ 18 A sample of...
Consider the following hypothesis test. H0: μ ≤ 12 Ha: μ > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.28. (a) Compute the value of the test statistic. (Round your answer to three decimal places.) (b) Use the t distribution table to compute a range for the p-value. p-value > 0.2000.100 < p-value < 0.200 0.050 < p-value < 0.1000.025 < p-value < 0.0500.010 < p-value < 0.025p-value <...
Consider the following hypothesis test. H0: μ ≤ 12 Ha: μ > 12 A sample of 25 provided a sample mean x = 14 and a sample standard deviation s = 4.32. (a) Compute the value of the test statistic. (Round your answer to three decimal places.) _______ (b) Use the t distribution table to compute a range for the p-value. a) p-value > 0.200 b) 0.100 < p-value < 0.200 c) 0.050 < p-value < 0.100 d) 0.025 <...
Consider the following hypothesis test. H0: μ ≤ 50 Ha: μ > 50 A sample of 60 is used and the population standard deviation is 8. Use the critical value approach to state your conclusion for each of the following sample results. Use α = 0.05. (Round your answers to two decimal places.) (a)x = 52.5 Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the...
Consider the following hypothesis test. H0: 1 - 2≤ 0 Ha: 1 - 2> 0 The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n 1 = 30 n 2 = 60 x 1 = 25.6 x 2 = 22.2 σ 1 = 5.2 σ 2 = 6 a. What is the value of the test statistic (round to 2 decimals)? b. What is the p-value (round to 4 decimals)? Use z-table. Use z-value rounded to...
Consider the following hypotheses: H0: μ = 19 HA: μ ≠ 19 The population is normally distributed. A sample produces the following observations: (You may find it useful to reference the appropriate table: z table or t table) 20 23 17 21 21 24 23 Click here for the Excel Data File a. Find the mean and the standard deviation. (Round your answers to 2 decimal places.) b. Calculate the value of the test statistic. (Round intermediate calculations to...
Consider the following hypothesis test. H0: p = 0.45 Ha: p ≠ 0.45 A sample of 200 provided a sample proportion p = 0.443. (a) Compute the value of the test statistic. (b) What is the p-value? (c) At α = 0.05, what is your conclusion? (d) What is the rejection rule using the critical value? What is your conclusion?
Exercise 9-39 Algo Consider the following hypotheses: H0: μ = 20 HA: μ ≠ 20 The population is normally distributed. A sample produces the following observations: (You may find it useful to reference the appropriate table: z table or t table) 24 20 24 21 21 24 19 Click here for the Excel Data File a. Find the mean and the standard deviation. (Round your answers to 2 decimal places.) b. Calculate the value of the test statistic. (Round...
Consider the following hypothesis test. H0: μ ≥ 10 Ha: μ < 10 The sample size is 155 and the population standard deviation is assumed known with σ = 5. Use α = 0.05. (a) If the population mean is 9, what is the probability that the sample mean leads to the conclusion do not reject H0? (Round your answer to four decimal places.) (b) What type of error would be made if the actual population mean is 9 and...
Consider the following hypotheses: H0: μ ≥ 160 HA: μ < 160 The population is normally distributed. A sample produces the following observations: 152 138 151 144 151 142 Conduct the test at the 1% level of significance. (You may find it useful to reference the appropriate table: z table or t table) a. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and...
You may need to use the appropriate appendix table or technology to answer this question Consider the following hypothesis test H0: p = 0.20 Ha: p # 0.20 A sample of 400 provided a sample proportion p = 0.185 (a) Compute the value of the test statistic. (Round your answer to two decimal places.) (b) What is the p-value? (Round your answer to four decimal places.) p-value- (C) 0.05, what is your conclusion? 0 Reject H0. There is insufficient evidence...