Question

In: Statistics and Probability

To test Upper H 0 : mu equals20 versus Upper H 1 : mu less than20,...

To test Upper H 0 : mu equals20 versus Upper H 1 : mu less than20, a simple random sample of size nequals 19 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d).

(a) If x overbar = 18 and s= 4.2 , compute the test statistic. (Round to two decimal places as needed.)

(b) Draw a t-distribution with the area that represents the P-value shaded. Which of the following graphs shows the correct shaded region?

(c) Approximate the P-value.

(d) If the researcher decides to test this hypothesis at the a= 0.05 level of significance, will the researcher reject the null hypothesis?

Expert Solution

Solution:
The provided sample mean is x̄ = 18 and the known population standard deviation is

s = 4.2, and the sample size is n = 19.

Null and Alternative Hypotheses:
The following null and alternative hypotheses need to be tested:

Ho: μ = 20
Ha: μ < 20
This corresponds to a one tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

a) Test statistic:

t= -2.08

b) Area of p-value :

c)
Using the P-value approach: The p-value is p = 0.0263, ..using excel formula, =TDIST(2.08,18,1)

and since p = 0.0263< 0.05, it is concluded that the null hypothesis is rejected

d)Conclusion: It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is less than 20, at the 0.05 significance level.

orchestra answered 1 year ago

To test Upper H 0 : mu equals60 versus Upper H 1 : mu less than60,...

To test Upper H 0 : mu equals60 versus Upper H 1 : mu less than60, a random sample of size nequals 25 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. (a) If x overbar =57.7and s=14.6, compute the test statistic. (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the a= 0.1 level of significance, determine the critical value(s). Although technology or...

To test Upper H 0: mu equals 50 versus Upper H 1: mu less than 50,...

To test Upper H 0: mu equals 50 versus Upper H 1: mu less than 50, a random sample of size n equals 22 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d) below. LOADING... Click here to view the t-Distribution Area in Right Tail. (a) If x over bar equals 47.1 and s equals 12.9, compute the test statistic. t 0 equals nothing (Round to three decimal places as needed.)

To test Upper H 0 : sigma equals 2.4 versus Upper H 1 : sigma greater...

To test Upper H 0 : sigma equals 2.4 versus Upper H 1 : sigma greater than 2.4, a random sample of size n equals 17 is obtained from a population that is known to be normally distributed. Complete parts (a) through (d). (a) If the sample standard deviation is determined to be s equals 2.3, compute the test statistic. chi Subscript 0 Superscript 2equals nothing (Round to three decimal places as needed.) (b) If the researcher decides to test...

To test Upper H 0: pequals0.60 versus Upper H 1: pless than0.60, a simple random sample...

To test Upper H 0: pequals0.60 versus Upper H 1: pless than0.60, a simple random sample of nequals450 individuals is obtained and xequals252 successes are observed. (a) What does it mean to make a Type II error for this test? (b) If the researcher decides to test this hypothesis at the alphaequals0.05 level of significance, compute the probability of making a Type II error, beta, if the true population proportion is 0.56. What is the power of the test? (c)...

To test Upper H 0: muequals100 versus Upper H 1: munot equals100, a simple random sample...

To test Upper H 0: muequals100 versus Upper H 1: munot equals100, a simple random sample size of nequals16 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). LOADING... Click here to view the t-Distribution Area in Right Tail. (a) If x overbarequals105.1 and sequals8.8, compute the test statistic. tequals nothing (Round to three decimal places as needed.) (b) If the researcher decides to test this hypothesis at the alphaequals0.01 level of significance, determine...

1. Suppose a researcher is testing the hypothesis Upper H 0: pequals0.6 versus Upper H 1:...

1. Suppose a researcher is testing the hypothesis Upper H 0: pequals0.6 versus Upper H 1: p less than0.6 and she finds the?P-value to be 0.24. Explain what this means. Would she reject the null?hypothesis? Why? Choose the correct explanation below. If the?P-value for a particular test statistic is 0.24, she expects results no more extreme than the test statistic in about 24 of 100 samples if the null hypothesis is true. If the?P-value for a particular test statistic is...

Consider the hypotheses below. Upper H 0: mu greater than or equals 65 Upper H 1:...

Consider the hypotheses below. Upper H 0: mu greater than or equals 65 Upper H 1: mu less than 65 Given that x overbar equals 57.3, s equals 9.7, nequals25, and alphaequals0.10, complete parts a and b below. a) What conclusion should be drawn? Determine the critical value(s). The critical value(s) is(are) nothing. (Round to three decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic, t Subscript x overbar. t Subscript x overbarequals...

Test the hypothesis using the P-value approach. Upper H 0 : p equals 0.50 versus Upper...

Test the hypothesis using the P-value approach. Upper H 0 : p equals 0.50 versus Upper H 1 : p less than 0.50 n equals 150 comma x equals 66 comma alpha equals 0.10 Perform the test using the P-value approach. P-valueequals nothing (Round to four decimal places as needed.)

Consider the following hypothesis test: H(0): mu ≥ 10 H(a): mu < 10 The sample size...

Consider the following hypothesis test: H(0): mu ≥ 10 H(a): mu < 10 The sample size is 120 and the population standard deviation is assumed known with σ = 5. Use alpha = .05. If the population mean is 9, what is the probability of making a Type II error if the actual population mean is 8 (to 4 decimals)? Please provide the appropriate formula in excel for solving this problem.

To test Upper H 0H0: muμequals=100 versus Upper H 1H1: muμnot equals≠100, a simple random sample...

To test Upper H 0H0: muμequals=100 versus Upper H 1H1: muμnot equals≠100, a simple random sample size of nequals=1616 is obtained from a population that is known to be normally distributed. Answer parts (a)-(d). LOADING... Click here to view the t-Distribution Area in Right Tail. (a) If x overbarxequals=105.8105.8 and sequals=9.39.3, compute the test statistic. tequals= nothing (Round to three decimal places as needed.)

Question

To test Upper H 0 : mu equals20 versus Upper H 1 : mu less than20,...

Solutions

Expert Solution

Related Solutions

To test Upper H 0 : mu equals60 versus Upper H 1 : mu less than60,...

To test Upper H 0: mu equals 50 versus Upper H 1: mu less than 50,...

To test Upper H 0 : sigma equals 2.4 versus Upper H 1 : sigma greater...

To test Upper H 0: pequals0.60 versus Upper H 1: pless than0.60, a simple random sample...

To test Upper H 0: muequals100 versus Upper H 1: munot equals100, a simple random sample...

1. Suppose a researcher is testing the hypothesis Upper H 0: pequals0.6 versus Upper H 1:...

Consider the hypotheses below. Upper H 0: mu greater than or equals 65 Upper H 1:...

Test the hypothesis using the P-value approach. Upper H 0 : p equals 0.50 versus Upper...

Consider the following hypothesis test: H(0): mu ≥ 10 H(a): mu < 10 The sample size...

To test Upper H 0H0: muμequals=100 versus Upper H 1H1: muμnot equals≠100, a simple random sample...

Question

To test Upper H 0 ​: mu equals20 versus Upper H 1 ​: mu less than20​,...

Solutions

Expert Solution

Related Solutions

To test Upper H 0 : mu equals20 versus Upper H 1 : mu less than20,...