6. A manufacturer makes a particular car part that is supposed to have a mean weight of 30 g. An angry customer suspects (claims) that the mean weight is actually less than 30 g. The mean weight of a random sample of 25 of these car parts is 29.2 g with a 0n standard deviation of 4.2 g. The sample is normally distributed. At the 0.05 significance level, test the customer's claim that the sample is from a population where the mean weight is less than 30 g. a) State the claim, null hypothesis and alternative hypothesis. Claim: Ho: H1: te td bni (d b) Find the t-statistic. slon on for thbtabo reti c) Find the p-value. pel f) Do you reject the null or fail to reject the null? Explain your answer either using your p-value or t-statistic and critical value. d) Interpret the results of your hypothesis test. Specifically, is there evidence to support the angry customers claim that the mean of the population is less than 30? Explain.

A psychology graduate student wants to test the claim that there is a significant difference between the IQs of spouses. To test this claim, she measures the IQs of 9 married couples using a standard IQ test. The results of the IQ tests are listed in the following table. Using a 0.02 level of significance, test the claim that there is a significant difference between the IQs assuming that the population distribution of the paired differences is approximately normal. Let the spouse 1 group be Population 1 and let the spouse 2 group be Population 2. IQs of Married Couples Spouse 121 98 108 119 101 108 111 127 103 1 Spouse 105 114 98 105 107 124 103 123 95 Copy Data Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. () = Prd: °H Prt: "H

Let's assume that the distribution of gas on a given day in a town is normally distributed with mean of $4.3371 with a standard deviation of $0.4192. What proportion of gas stations are charging less than $3.4387? 98.3949% 0.8026% 1.6051% 3.2103% O 0%

An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons. When testing the hypothesis (at the 1% level of significance) that there is no difference between the average yields using the different fertilizers, what is the null and alternative hypotheses?

Assume the average amount of caffeine consumed daily by adults is normally distributed with a mean of 260 mg and a standard deviation of 48 mg. In a random sample of 600 ​adults, how many consume at least 320 mg of caffeine​ daily?

A psychology graduate student wants to test the claim that there is a significant difference between the IQs of spouses. To test this claim, she measures the IQs of 9 married couples using a standard IQ test. The results of the IQ tests are listed in the following table. Using a 0.10 level of significance, test the claim that there is a significant difference between the IQs assuming that the population distribution of the paired differences is approximately normal. Let the spouse 1 group be Population 1 and let the spouse 2 group be Population 2. Spouse 1 Spouse 2 IQs of Married Couples 124 113 97 123 121 101 128 116 96 126 119 100 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places. 124 111 127 113 107 111

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…

An agricultural company is trying to decide which type of fertilizer to use on its crops. The company concerned with the average yield on its crops as well as the variance of their yields. In a sample of 41 different fields with using fertilizer A, the average crop yield per acre is 185 tons with a standard deviation of 35 tons. In a separate sample of 61 different fields using fertilizer B, the average crop yield is 175 tons with a standard deviation of 28 tons. When testing the hypothesis (at the 5% level of significance) that the variance of one of these yields is significantly larger than the other, what is the null and alternative hypotheses?

Suppose that water usages in American showers are normally distributed, with an average shower using 20 gallons, and a standard deviation of 3.2 gallons. Estimate the percentage of showers that used (a) between 13.6 and 26.4 gallons. % (b) more than 26.4 gallons. % (c) less than 10.4 gallons. % (d) between 16.8 and 29.6 gallons. %

Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of women