5.3 Population Variances Are Not Kn ssumptions: Populations are normal and small samples deviations are assumed to be equal. est statistic: (x- ) - D II

The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers?                                                                                                                                                                                                                                                                    Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal.   Teacher 1 Teacher 2 ?̅1 =  473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18   a. State the null and alternate hypotheses (write it mathematically) and write your claim.   b. Find the test statistic        c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…

Q2: Serum amylase determinations were made on a sample of 15 apparently healthy subjects in the Electricity Power Plant of Nasriya January 2010. The sample yielded a mean of 96 and a standard deviation of 35 units/100ml. Estimate the true mean of serum amylase in the healthy population of Nasriya.

#4data: 0.06, 0.11, 0.16, 0.15, 0.14, 0.08, 0.15. Use the sample data from #4 to construct a 98% confidence interval estimate for the standard deviation of the amount nitrogen-oxide emission for all cars.

A random sample of 10 subjects have weights with a standard deviation of 11.9848 kg . What is the variance of their weights ? Be sure to include the appropriate units with the result .

A new material will replace the old material only if there is significant evidence that the mean strength of the new material is more than 2 units higher than the mean strength of the old material.        Sample from new material:     mean  is  98.064   ,     SD  is   5.6     and sample size is 13 Sample from old material:       mean  is  95.282   ,     SD  is   5.8      and sample size is 78 We do not know population standard deviations. Consider the test           ?0:????−????=2H0:μnew−μold=2   vs.  ?0:????−????>2H0:μnew−μold>2  What is the p-value?       (Hint:  best to use software, or else the Desmos Calculator for the 2 sample T and Z test)  Give as a decimal between 0 and 1 accurate to at least 4 decimal places.

The mean age of 31 slot mechanic player is 51.3 years, and the standard deviation is 6.8 years.the mean age of a different sample of 35 roulette player is 54.8 year and standard deviation is 3.2 years. Can it be concluded at alpha = 0.01 that the mean age of slot machine players is less than those players roulette? Assume the variance are equal Step 1= Step 2= Step 3= Step 4=

2. A pet association claims that the mean annual costs of food for dogs and cats are the same. The results for samples of the two types of pets are shown in the following table. On wished to test the claim. Assume both populations follow normal distributions Dogs Cats 21 - 16 T1= 239 n2 = 18 Iz= 203 S1 = 32 82 =28 with equal variances. Which of the following formula should be used to calculate the standardized test statistic? (a) Z = (21-32)- Do lu A n2 = (E1-2)-Do (b) Z V n1+2 (c) T (1-2)-Do (21-1)a7+(n2-1)s I1 11+11タ-3 V 1'n2 (d) T = d- Do sp/Vn (e) Z

Paramesan cheese is aged for an average of 24 months to allow it to develop the desire richness in flavor the standard deviation for the length of time Parmesan cheese is aged is 3.7 months How long would Parmesan cheese have to be aged in order to be in the 90th percentile? Assume that the data is normally distributed