The mean SAT score in mathematics, u, is 596. The standard deviation of these scores is 47. A special preparation course claims that its graduates will score higher, on average, than the mean score 596. A random sample of 90 students completed the course, and their mean SAT score in mathematics was 608. At the 0.05 level of significance, can we conclude that the preparation course does what it claims? Assume that the standard deviation of the scores of course graduates is also 47. Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. Ho :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the critical value. (Round to three or more decimal places.) (e) Can we support the preparation course's claim that its graduates score higher in SAT? OYes ONo

An IQ test has a mean of 96 and a standard deviation of 15. Which is more​ unusual, an IQ of 81 or an IQ of 120​?

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.4 inches, with estimated standard deviation s = 2.7 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. Solve the problem using the critical region method of testing (i.e., traditional method). (Round the your answers to three decimal places.)   test statistic =   critical value =   State your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the average fish length is less than 19 inches.Reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches.    Fail to reject the null hypothesis, there is…

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05.   a) Estimate the P-value. select one:P-value > 0.0100.0010 < P-value < 0.010 0.250 < P-value < 0.00100.125 < P-value < 0.250P-value < 0.125 b) Sketch the sampling distribution and show the area corresponding to the P-value. c) will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ??At the ? = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the ? = 0.05 level, we reject the null hypothesis and…

A successful basketball player has a height of 6 feet 11 ​inches, or 211 cm. Based on statistics from a data​ set, his height converts to the z score of 5.17. How many standard deviations is his height above the​ mean?

A researcher believes the mean weight of males sulcata tortoises is more than 205 pounds.  She samples 18 males sulcatas and find their mean to be 216.2 pounds with a standard deviation of 13.5pounds.  Find the p-value p =

The distribution of the student heights at a large college is approximately bell shaped. If the mean height is 66 inches,and approximately 95% of the heights fall between 32 and 100 inches, then, the standard deviation of the heightdistribution is approximately equal to

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is ? = 19 inches. However, a survey reported that of a random sample of 51 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.5 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than ? = 19 inches? Use ? = 0.05. (a)What is the level of significance? =__   State the null and alternate hypotheses. A-H0: ? = 19 in; H1: ? ≠ 19 in B-H0: ? < 19 in; H1: ? = 19 in  C-H0: ? = 19 in; H1: ? < 19 in D-H0: ? = 19 in; H1: ? > 19 in E-H0: ? > 19 in; H1: ? = 19 in (b)What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. A-The Student's t, since the sample size is large and ? is known. B-The standard normal, since the sample size is large and ? is known. C-The…

In the class of 2019, more than 1.6 million students took the SAT. The distribution of scores on the math section (out of 800) is approximately normal with a mean of 528 and standard deviation of 117.  What proportion of students earned scores between 500 and 600 on the SAT math test?

A reading class can read an mean of 175 words per minute and a population standard deviation of 20 words per minutes.  The top 3% of the class is to receive a special award for a random sample of 49 students. What is the minimum average number of words per minute a student would need to read in order to get the award for a random sample of 49 students?  Assume the data is normally distributed.