Question

Many consumers pay careful atention to contents on packaged foods when making purchases, so stated nutri- that a random sample of n 12 frozen dinners of a Suppe was selected and the calorie content of each one certai n type ned. Below are the resulting observations, along with a boxplot and a normal probability plot. 244 239 242 265 245 259 225 226 251 233 265 255 245 235 boxplot suggest that actual mean content differs from the stated value? Explain your reasoning c. Carry out a formal test of the hypotheses suggested in Part (b) 225 265 255 245 235 225 1.5 0.5 0.5 Normal score Is it reasonable to test hypotheses about the popula- mean calorie content u using a one-sample t test? Explain why or why not. b. The a. manufacturer claims that the mean calorie content for this particular type of frozen dinner is 240. Does the

Answer 1

a) It is correct to choose one sample t-test because the sample is taken from a large population and the plot also show that the distribution is approximately normal and hence assumed as normal distribution but the sample size is less than 30 so t- distribution is assumed .

b) No, because the box plot appears a normally distributed from naked eye view and also the median is around 240 so, we cannot say that the mean differs from 240.

c) Since the mean is calculated as

1

z = 244.33

z = 244.33

and Sample standard deviation is calculated as

N -1 N-1 -(255-244.33333333333)2(233 -244.33333333333)2 12-1 1686.6666666667 153.33333333333 s : .. 153.33333333333 12.382783747338

The Hypotheses are

Ho:μ=240

Ha : μ 240

Significance level is assumed as 0.05 since it is not given in ques

rejection region:

Reject Ho if |T| >t _{0.05, 11} =2.20 , where 11= degree of freedom =n-1=12-1=11

Test statistic:

x-μ 1.21 V12 7t

P-value:

P-value associated with t Score calculated above as

0.1<p-value<0.5

Conclusion:

Since T< t _0.05,11 =2.20 and P-value > 0.05 hence we fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that mean differs from 240 at 0.05 level of significance.

T-table used for calculation as

Numbers in each row of the table are values on a t-distribution with (df) degrees of freedom for selected right-tail (greater-than) probabilities (p) t (p, df) df/p0.40 0.25 0.10 0.05 0.025 0.01 0.005 0.0005 1 0.324920 1.000000 3.077684 6.31375212.70620 31.82052 63.65674 636.6192 2 0.288675 0.816497 1.885618 2.919986 4.30265 6.964569.92484 31.5991 3 0.276671 0.7648921.637744 2.353363 3.182454.54070 584091 12.9240 0.270722 0.7406971.533206 2.131847 2.77645 0.267181 0.726687 14758842015048 2.57058 0.264835 0.717558 1.4397561.943180 2.4469 3.14267 3.70743 63167 0.711142 1.414924 1894579 2.36462 4.60409 8.6103 364934.03214 6.86 5 0 3.3 88 7 0.26 2.99795 3.49948 5.4079 8 0.261921 0.7063871.396815 1.8595482.3060 3.35539 5.0413 9 0.260955 0.702722 1.383029 1.833113 2.26216 2.82144 3.24984 4.7809 10 0.260185 0.699812 .372184 1.812461 11 0.259556 0.697445 1.363430 1.795885 814 2.76377 3.16927 4.5 2.228 869 2.20099 2.71808 3.105814.4370 68100 3.05454 43178 12 0.259033 0.695483 356217 1.782288 788 2.6 91 0.693829 1350171 1.770933 2.16037 14 0.258213 0.692417 1.345030 1.761310 2.14479 15 0.257885 0.691197 1.340606 1.753050 2.13145 13 0.2585 2.65031 3.012284.2208 2.976844.1405 2.62449 2 94671 4.0728 16 0.257599 0.690132 1.336757 1.745884 2.11991 2.58349 2.92078 4.0150 17 0.257347 0.689195 1.333379 1.739607 2.10982 18 0.257123 0.688364 1.330391 1.734064 2.10092 2.56693 2.89823 3.9651 2.55238 2.878443.9216 19 0.256923 0.687621327728 1.729133 2.09302 2.53948 2.860933.8834 20 0.256743 0.686954 1.325341 1.724718 2.08596 21 0.256580 0.686352 1.323188 1.720743 2.07961 2.52798 2.845343.8495 2.51765 283136 3.8193 22 0.256432 0.685805 1.321237 1.717144 2.07387 2.508322.81876 3.7921 297 0.685306 1.319460 1.713872 2.068 23 0.2562 662.49987 2.80734 3.7676 24 0.256173 0.6848501317836 1.710882 2.063902.49216 2.796943.7454 0.256060 0.6844301.316345 1.708141 2.05954 2.48511 2.78744 3.7251 1.314972 1.705618 2.05553 26 0.2559550.6840431 2.47863 2.778713.7066 27 0.255858 0.683685 1.313703 .7032882.05183 2.47266 2.770683.6896 28 0.255768 0.683353 1.312527 17011312.04841 2.46714 2.76326 3.6739 29 0.2556840.683044 1.311434 1.699127 2.04523 2.462022.75639 3.6594 30 0.255605 0.682756 1.310415 .697261 2.04227 2.45726 2.75000 3.6460 z 0.2533470.674490 1.281552 1.6448541.959962.32635 2.57583 3.2905 80% 90% 95% 98% 99% 99.9% CI